In this paper, we have investigated second Hankel determinants and FeketeSzeg? inequalities for some subclasses of Bi-univalent functions with respect to symmetric and Conjugate points which are subordinate to a shell...In this paper, we have investigated second Hankel determinants and FeketeSzeg? inequalities for some subclasses of Bi-univalent functions with respect to symmetric and Conjugate points which are subordinate to a shell shaped region in the open unit disc ?.展开更多
Two points of the infinite dimensional complex projective space CP∞ with homogeneous coordinates a = （a0, a1, a2, ） and b = （b0, b1, b2, ）, respectively, are conjugate if and only if they are complex orthogonal, ...Two points of the infinite dimensional complex projective space CP∞ with homogeneous coordinates a = （a0, a1, a2, ） and b = （b0, b1, b2, ）, respectively, are conjugate if and only if they are complex orthogonal, i.e., ab = ∞∑j=0 ajbj = 0. For a complete ortho-normal system φ（t） = （φ0（t）, φ1（t）, φ2（t）, ） of L2H（D）, the space of the holomorphic and absolutely square integrable functions in the bounded domain D of Cn, φ（t）, t ∈ D, is considered as the homogeneous coordinate of a point in CP∞. The correspondence t →φ（t） induces a holomorphic imbedding ιφ ： D → CP∞. It is proved that the Bergman kernel K（t, v） of D equals to zero for the two points t and v in D if and only if their image points under ιφ are conjugate points of CP∞.展开更多
In this paper, the concept of the equidistant conjugate points of a triangle to the n-dimensional Euclidean space is extended. The concept of equidistant conjugate point in high dimensional simplex is defined, and the...In this paper, the concept of the equidistant conjugate points of a triangle to the n-dimensional Euclidean space is extended. The concept of equidistant conjugate point in high dimensional simplex is defined, and the property of the equidistant conjugate points of a triangle is generalized to high dimensional simplex.展开更多
In this article,we consider the entropy-expansiveness of geodesic flows on closed Riemannian manifolds without conjugate points.We prove that,if the manifold has no focal points,or if the manifold is bounded asymptote...In this article,we consider the entropy-expansiveness of geodesic flows on closed Riemannian manifolds without conjugate points.We prove that,if the manifold has no focal points,or if the manifold is bounded asymptote,then the geodesic flow is entropy-expansive.Moreover,for the compact oriented surfaces without conjugate points,we prove that the geodesic flows are entropy-expansive.We also give an estimation of distance between two positively asymptotic geodesics of an uniform visibility manifold.展开更多
We study conjugate points on a type of Khler manifolds, which are submanifolds of Grassmannian manifolds. And then we give the applications to the study of the index of geodesics and homotopy groups.
文摘In this paper, we have investigated second Hankel determinants and FeketeSzeg? inequalities for some subclasses of Bi-univalent functions with respect to symmetric and Conjugate points which are subordinate to a shell shaped region in the open unit disc ?.
基金Partially support by NSF of China (A01010501 and10731080)
文摘Two points of the infinite dimensional complex projective space CP∞ with homogeneous coordinates a = （a0, a1, a2, ） and b = （b0, b1, b2, ）, respectively, are conjugate if and only if they are complex orthogonal, i.e., ab = ∞∑j=0 ajbj = 0. For a complete ortho-normal system φ（t） = （φ0（t）, φ1（t）, φ2（t）, ） of L2H（D）, the space of the holomorphic and absolutely square integrable functions in the bounded domain D of Cn, φ（t）, t ∈ D, is considered as the homogeneous coordinate of a point in CP∞. The correspondence t →φ（t） induces a holomorphic imbedding ιφ ： D → CP∞. It is proved that the Bergman kernel K（t, v） of D equals to zero for the two points t and v in D if and only if their image points under ιφ are conjugate points of CP∞.
基金Supported by the Technological Project of Jiangxi Province Education Department(GJJ 08389)
文摘In this paper, the concept of the equidistant conjugate points of a triangle to the n-dimensional Euclidean space is extended. The concept of equidistant conjugate point in high dimensional simplex is defined, and the property of the equidistant conjugate points of a triangle is generalized to high dimensional simplex.
基金supported by NSFC(Grant Nos.11301305 and 11571207)the grant "2012KYTD" from Shandong University of Science and Technology+2 种基金supported by NSFC(Grant No.11101294)Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20111108120001)the grant of"Youxiu Rencai Peiyang Zizhu"(Class A)from the Beijing City
文摘In this article,we consider the entropy-expansiveness of geodesic flows on closed Riemannian manifolds without conjugate points.We prove that,if the manifold has no focal points,or if the manifold is bounded asymptote,then the geodesic flow is entropy-expansive.Moreover,for the compact oriented surfaces without conjugate points,we prove that the geodesic flows are entropy-expansive.We also give an estimation of distance between two positively asymptotic geodesics of an uniform visibility manifold.
基金supported by Science and Technology Projects of Beijing Municipal Commission of Education(Grant No.Z2011-008)supported by National Natural Science Foundation of China(GrantNo.11001148)
文摘We study conjugate points on a type of Khler manifolds, which are submanifolds of Grassmannian manifolds. And then we give the applications to the study of the index of geodesics and homotopy groups.
