Keyword: Geometry Of Geodesics : Search

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COMPLETE REAL HYPERSURFACES AND SPECIAL 𝕂-LINE BUNDLES IN 𝕂-HYPERBOLIC SPACES
- NOBUHIRO INNAMI,
- YOE ITOKAWA, and
- KATSUHIRO SHIOHAMA
International Journal of Mathematics01 Sep 2013
Preview Abstract
Using the geometry of geodesics, we discuss the global aspects of complete real hypersurfaces in hyperbolic spaces of constant holomorphic sectional curvature over any division algebra 𝕂. Our assumption is that the shape operator and the curvature transformation with respect to the normal unit have the same eigenspaces. Note that we do not assume constancy of the principal curvatures. Under this assumption, we give a complete global classification of such hypersurfaces. Since the argument is purely geometric, we need not vary the argument for different base algebras. The foliations of with totally geodesic leaves called 𝕂-lines play an important role.

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