Totally Real Minimal Submanifolds in a Quaternion Projective Space

Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. Shen are improved and generalized.

Some remarks on pseudo-umbilical totally real submanifolds in a complex projective space

This paper studies the relationship between the pseudo-umbilical totally real submanifolds and the minimal totally real submanifolds in a complex projective space. Two theo- rems which claim that some types of pseudo-umbilical totally real submanifolds must be minimal submanifolds are proved.

GEOMETRIC CONSTRUCTION OF ASSOCIATION SCHEMES FROM DEGENERATE QUADRICS INPROJECTIVE SPACES PG(2ν+δ+ι-1, Fq) FOR q ODD

Let Fq be a finite field with q elements, where q is a power of an odd prime,In this paperl the authors consider a projective space PG(2v + δ + l, Fq) with dimension 2v + δ + l, partitioned into an affine space AG(2v + δ + l, Fq) of dimension 2v + δ + l and a hyperplane H = PG(2v + δ + l - 1, Fq) of dimension 2v + δ + l - 1 at infinity, where l ≠0.The points of the hyperplane H are next partitioned into four subsets. A pair of points a and b of the affine space is defined to belong to class i if the line ab meets the subsct i of H. Finally, a family of four-class association schemes are constructed, and parameters are also computed.

A Note on Totally Real Riemannian Foliations with Parallelized Mean Curvature Vectors in a Complex Projective Space

We discussed a totally real Riemannian foliations with parallel mean curvature on a complex projective space.We carried out the divergence of a vector field on it and obtained a formula of Simons’type.

2-Harmonic Totally Real Submanifolds in a Complex Projective Space

In this paper, we discuss the relations between the 2-harmornic totally real submsnifold and the minimal totall real submanifold in the complex protective spsace, and obtain the pinching conductions for the second fundamental form and the Rieci curature of the 2-harmornic totally real submanifold in the complex projective space.

Mean Curvature Flow of Arbitrary Codimension in Complex Projective Spaces

Recently,Pipoli and Sinestrari[Pipoli,G.and Sinestrari,C.,Mean curvature flow of pinched submanifolds of CPn,Comm.Anal.Geom.,25,2017,799-846]initiated the study of convergence problem for the mean curvature flow of small codimension in the complex projective space CPm.The purpose of this paper is to develop the work due to Pipoli and Sinestrari,and verify a new convergence theorem for the mean curvature flow of arbitrary codimension in the complex projective space.Namely,the authors prove that if the initial submanifold in CPm satisfies a suitable pinching condition,then the mean curvature flow converges to a round point in finite time,or converges to a totally geodesic submanifold as t→∞.Consequently,they obtain a differentiable sphere theorem for submanifolds in the complex projective space.

On Totally Real Pseudo-Umbilical Submanifolds in a Complex Projective Space

Let M^n be a totally real submanifold in a complex projective space CP^(n+p).In this paper,we study the position of the parallel umbilical normal vector field of M^n in the normal bundle.By choosing a suitable frame field,we obtain a pinching theorem,in the case p>0, for the square of the length of the second fundamental form of a totally real pseudo-umbilical submanifold with parallel mean curvature vector.

On Complete Totally Real Pseudo-Umbilical Submanifolds in a Complex Projective Space

Let Mn be a totally real pseudo-umbilical submanifold in a complex projective space CPn＋p. In this paper, we study the position of completeness of Mn. By choosing a suitable frame field, we obtain a rigidity theorem such that Mn becomes totally umbilical submanifold and improve the related results.

Self-maps of p-local infinite projective spaces

Abstract Denote by z（p） （resp. Zp） the p localization （resp. p completion） of z. Then we have the canonical inclusion Z（p）→ zp. Let S2n-1（p） be the p-local （2n- 1）-sphere and let B2n（p） be a connected p-local space satisfying S2n-l（p）≌ΩB2n（p）, then H＊B2n（p）,Z（p）） = Z（p）[U] with ｜u｜ = 2n. Define the degree of a self-map f of B2n（p） to be k E Z（p） such that f＊（u） = ku. Using the theory of integer-valued polynomials we show that there exists a self-map of B2n（p） of degree k if and only if k is an n-th power in Zp.

Minimal two-spheres with constant curvature in the quaternionic projective space

In this paper we completely classify the homogeneous two-spheres,especially,the minimal homogeneous ones in the quaternionic projective space HPn.According to our classification,more minimal constant curved two-spheres in HPnare obtained than what Ohnita conjectured in the paper"Homogeneous harmonic maps into complex projective spaces.Tokyo J Math,1990,13:87–116".

The Eigen Functions of the Complex Projective Space

In the complex n-dimensional projective space CP^n. let λ_p(=4p(p+n)) be the eigen vaiue of the Laplace-Beltrami operator and H_p be the space of all eigen functions of eigen value λ_p. The reproducing kernel h_p(z, w) of H_p is constructed explicitly in this paper. and a system of complete orthogohal functions of H_p is construncted from h_p(z, w)(p=1,2…).

Vanishing Ideals of Projective Spaces over Finite Fields and a Projective Footprint Bound

We consider the vanishing ideal of a projective space over a finite field. An explicit set of generators for this ideal has been given by Mercier and Rolland. We show that these generators form a universal Gr¨obner basis of the ideal. Further we give a projective analogue for the so-called footprint bound, and a version of it that is suitable for estimating the number of rational points of projective algebraic varieties over finite fields. An application to Serre’s inequality for the number of points of projective hypersurfaces over finite fields is included.

Hypergeometric equations and weighted projective spaces

We compute the Hodge numbers of the polarised(pure) variation of Hodge structure V = grn-1WRn-1f!Z of the Landau-Ginzburg model f:Y → C mirror-dual to a weighted projective space wPn in terms of a variant of Reid's age function of the anticanonical cone over wPn.This implies,for instance,that wPn has canonical singularities if and only if hn-1,0V = 1.We state a conjectural formula for the Hodge numbers of general hypergeometric variations.We show that a general fibre of the Landau-Ginzburg model is birational to a Calabi-Yau variety if and only if a general anticanonical section of wP is Calabi-Yau.We analyse the 104 weighted 3-spaces with canonical singularities,and show that a general anticanonical section is not a K3 surface exactly in those 9 cases where a generic fibre of the Landau-Ginzburg model is an elliptic surface of Kodaira dimension 1.

ON THE CENTRAL LIMIT THEOREM IN PRODUCT SPACES

Suppose that E and F are separable Banach spaces, X and Y are independent symmetric E and F-valued random vectors respectively. This paper is devoted to the study of the central limit theorem for X Y in the injective and projective tensor product spaces E F and E F. Special attention is paid to l2 l2. In addition, two counter-examples are given.

THE CONTRACTION LINEAR METRIC PROJECTIONS IN L_p SPACES

In this paper, we study the contraction linearity for metric projection in L p spaces. A geometrical property of a subspace Y of L p is given on which P Y is a contraction projection.

Korean Participation in the Galex Ultraviolet Space Telescope Project

The Center for Space Astrophysics at Yonsei university, Seoul, Korea, is actively participating in the development and operation of the Galaxy Evolution Explorer (GALEX), a NASA ultraviolet space telescope project to be launched in late 2001. As the first official case of NASA Korea cooperation on major space science program, this project will greatly expand the capability of Korean astronomy into space based operations.

China Space Benefit Project

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A Creation Model from the Gell-Mann Standard Model to the Creation of Bio Cells: Based on the Assumption of Homogeneous 5D Space-Time Universe

In this paper, we briefly go over the homogeneous 5D model field theory: from the 5D space-time inception, to its quantum field solutions given in terms of Higgs vacuum, filled with magnetic monopole bose fields of all energies. Then through the space dimension reduction projections, the Gell-Mann standard model was obtained as well as a quantum to Classical connection was made via introducing Bose distribution to the monopoles to obtain the Perelman entropy and Ricci Flow mappings. This provided us a picture to the creation of Astronomical objects, from galaxies to stars and planets. This method of splitting the monopole energy into ranges is extended to show that below the basic rest mass range of the electron and Quark, it still can be applied to explaining for the creation of the chemical elements periodic table. But perhaps the most interesting is in the lowest hundreds of Hz energy range, obtained from yet another 3 fold space symmetry breaking, into 2D × 1D, producing bio nitrogenous bases composed of 3 Carbon 12 in hexagon structures, due to preservation of the 1D monopole standing waves of this low frequencies. From that by imposing gauge changes the monopole states into DNA spectra. Since such spectra states retain the DLRO, it induces formation of charge carriers periodicity in a spherical bio cell.. It was then argued that due to cell’s surface proteins, the structure must contain partial filled VB, with “p” state hole density, and empty CB, separated from VB by a positive band gap. Such band structures resemble known HTC Cuprate ceramics. Since the HTC goes through a Superconductivity transition via the simultaneous bose exciton condensation, providing a Coulomb pressure, which reduces the band gap substantially, and induces the ODLRO transition of the hole density. The same obviously applies to the bio cells. Because of the near continuous exciton levels generated, a matching to the DNA spectra then can always occur by selective choices of proteins on the cell surface. Judging from a numerical study, we did years ago on YBCO, with doping. We found with a large enough VB hole density, the exciton induced superconducting gap can easily lead to Tc in the room temperature range. In fact by EMF excitation can increase the exciton pressure and trigger the ODLRO transition Tc upward. In fact, numerical results then suggest there do exist coherent EMF spectra from three key elements: Water, Carbon and Hydrogen, together with Oxygen, as studied over the years by numerous people, starting from Schrödinger to most recently Geesink.

ON THE EXISTENCE OF SINGULAR DIRECTIONS OF HOLOMORPHIC MAPS FROM THE UNIT DISK INTO P^n(C)

This article proves the existence of Julia directions of value distribution of holomorphic mapping f from the unit disk into the n-dimensional complex projective spacePn（C） under the assumption limsupT（r,f）/log 1/1-r = ＋∞ for hypersurfaces in general position. A heuristic principle concerning the existence of Julia directions of holomorphic mappings from the unit disk into Pn（C） is given also.

ON THE SINGULAR DIRECTIONS OF VALUE DISTRIBUTION OF HOLOMORPHIC CURVES IN P^n(C)

This article proves the existence of singular directions of value distribution theory for some transcendental holomorphic curves in the n-dimensional complex projective space P^n（C）.. An example is given to complement these results.