We are interested in a quantum mechanical system on a triply punctured two-sphere surface with hyperbolic metric. The bound states on this system are described by the Maass cusp forms （MCFs） which are smooth square ...We are interested in a quantum mechanical system on a triply punctured two-sphere surface with hyperbolic metric. The bound states on this system are described by the Maass cusp forms （MCFs） which are smooth square integrable eigenfunctions of the hyperbolic Laplacian. Their discrete eigenvalues and the MCF are not known analytically. We solve numerically using a modified Hejhal and Then algorithm, which is suitable to compute eigenvalues for a surface with more than one cusp. We report on the computational results of some lower-lying eigenvalues for the triply punctured surface as well as providing plots of the MCF using GridMathematica.展开更多
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-sphere...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".展开更多
In this paper the author derives a geometric characterization of totally isotropic Willmore two-spheres in S^(6), which also yields to a description of such surfaces in terms of the loop group language. Moreover, appl...In this paper the author derives a geometric characterization of totally isotropic Willmore two-spheres in S^(6), which also yields to a description of such surfaces in terms of the loop group language. Moreover, applying the loop group method, he also obtains an algorithm to construct totally isotropic Willmore two-spheres in S^(6). This allows him to derive new examples of geometric interests. He first obtains a new, totally isotropic Willmore two-sphere which is not S-Willmore(i.e., has no dual surface) in S^(6). This gives a negative answer to an open problem of Ejiri in 1988. In this way he also derives many new totally isotropic, branched Willmore two-spheres which are not S-Willmore in S^(6).展开更多
We study conformal minimal two-spheres immersed into the quaternionic projective spaceℍP^(n) by using the twistor map.We present a method to construct new minimal two-spheres with constant curvature inℍP^(n),based on ...We study conformal minimal two-spheres immersed into the quaternionic projective spaceℍP^(n) by using the twistor map.We present a method to construct new minimal two-spheres with constant curvature inℍP^(n),based on the minimal property and horizontal condition of Veronese map in complex projective space.Then we construct some concrete examples of conformal minimal two-spheres inℍP^(n) with constant curvature 2/n,n=4,5,6,respectively.Finally,we prove that there exist conformal minimal two-spheres with constant curvature 2/n inℍP^(n)(n≥7).展开更多
文摘We are interested in a quantum mechanical system on a triply punctured two-sphere surface with hyperbolic metric. The bound states on this system are described by the Maass cusp forms （MCFs） which are smooth square integrable eigenfunctions of the hyperbolic Laplacian. Their discrete eigenvalues and the MCF are not known analytically. We solve numerically using a modified Hejhal and Then algorithm, which is suitable to compute eigenvalues for a surface with more than one cusp. We report on the computational results of some lower-lying eigenvalues for the triply punctured surface as well as providing plots of the MCF using GridMathematica.
基金supported by National Natural Science Foundation of China(Grant Nos.11471299,11401481 and 11331002)。
文摘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".
基金supported by the National Natural Science Foundation of China(Nos.11971107,11571255).
文摘In this paper the author derives a geometric characterization of totally isotropic Willmore two-spheres in S^(6), which also yields to a description of such surfaces in terms of the loop group language. Moreover, applying the loop group method, he also obtains an algorithm to construct totally isotropic Willmore two-spheres in S^(6). This allows him to derive new examples of geometric interests. He first obtains a new, totally isotropic Willmore two-sphere which is not S-Willmore(i.e., has no dual surface) in S^(6). This gives a negative answer to an open problem of Ejiri in 1988. In this way he also derives many new totally isotropic, branched Willmore two-spheres which are not S-Willmore in S^(6).
基金This work was supported in part by the National Natural Science Foundation of China(Grant No.11871450).
文摘We study conformal minimal two-spheres immersed into the quaternionic projective spaceℍP^(n) by using the twistor map.We present a method to construct new minimal two-spheres with constant curvature inℍP^(n),based on the minimal property and horizontal condition of Veronese map in complex projective space.Then we construct some concrete examples of conformal minimal two-spheres inℍP^(n) with constant curvature 2/n,n=4,5,6,respectively.Finally,we prove that there exist conformal minimal two-spheres with constant curvature 2/n inℍP^(n)(n≥7).
