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
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).
