Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Real hypersurfaces and complex submanifolds in complex projective space

Author: Makoto Kimura
Journal: Trans. Amer. Math. Soc. 296 (1986), 137-149
MSC: Primary 53C40
MathSciNet review: 837803
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $M$ be a real hypersurface in ${P^n}({\mathbf {C}})$ be the complex structure and $\xi$ denote a unit normal vector field on $M$. We show that $M$ is (an open subset of) a homogeneous hypersurface if and only if $M$ has constant principal curvatures and $J\xi$ is principal. We also obtain a characterization of certain complex submanifolds in a complex projective space. Specifically, ${P^m}({\mathbf {C}})$ (totally geodesic), ${Q^n},{P^1}({\mathbf {C}}) \times {P^n}({\mathbf {C}}),SU(5)/S(U(2) \times U(3))$ and $SO(10)/U(5)$ are the only complex submanifolds whose principal curvatures are constant in the sense that they depend neither on the point of the submanifold nor on the normal vector.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 53C40

Retrieve articles in all journals with MSC: 53C40

Additional Information

Keywords: Real hypersurfaces, complex submanifolds, focal sets, tubes, shape operators
Article copyright: © Copyright 1986 American Mathematical Society