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- W1563987584 abstract "The idea of constant width has been developed in a somewhat differentspirit, as a topic in differentialgeometry, and the concept of transnormality has been introduced as the generalized one of constant width in a Riemannian manifold. Let M be a connected complete hypersurface of a connected complete Riemannian manifold M. For each igM, there exists,up to parametrization, a unique geodesic zx of M which intersectsM orthogonally at x. M is called a transnormal hypersurface of M it, for each pair x,y<E.M, the relationyr for xjgM, x~y means that yE.rx. Then we can consider the quotient space M―Mj~ with the quotient topology with respect to thisrelation. We call M an r-transnormal hypersurface if the natural projection of M onto M is an r-fold covering map. Topological structures of transnormal submanifolds are full of interest and have been investigated from various angles (for example, see [3]). On the other hand, differentialgeometric structures of 2-transnormal hypersurfaces in a space form have been given in [2] and [4]. Recentry, the author has studied in [5] differentialgeometric structures of compact 2-transnormal hypersurfaces in a complex space form. The purpose of this paper is to generalize the result in [5] to the case where 2-transnormal hypersurfaces are complete. Namely we shall prove that 2-transnormal hypersurfaces in a Kaehler manifold of negative constant holomorphic sectionalcurvature are tubes over some submanifolds or geodesic hyperspheres if any principal curva-" @default.
- W1563987584 created "2016-06-24" @default.
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- W1563987584 date "1987-12-01" @default.
- W1563987584 modified "2023-09-25" @default.
- W1563987584 title "Complete 2-transnormal hypersurfaces in a Kaehler manifold of negative constant holomorphic sectional curvature" @default.
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- W1563987584 doi "https://doi.org/10.21099/tkbjm/1496160586" @default.
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