An estimate of sectional curvatures of hypersurfaces with positive Ricci curvatures
نویسندگان
چکیده
منابع مشابه
Totally umbilical radical transversal lightlike hypersurfaces of Kähler-Norden manifolds of constant totally real sectional curvatures
In this paper we study curvature properties of semi - symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,widetilde g)$ of a K"ahler-Norden manifold $(overline M,overline J,overline g,overline { widetilde g})$ of constant totally real sectional curvatures $overline nu$ and $overline {widetilde nu}$ ($g$ and $widetilde g$ are the induced metrics on $M$...
متن کاملConvex hypersurfaces of prescribed curvatures
For a smooth strictly convex closed hypersurface Σ in R, the Gauss map n : Σ → S is a diffeomorphism. A fundamental question in classical differential geometry concerns how much one can recover through the inverse Gauss map when some information is prescribed on S ([27]). This question has attracted much attention for more than a hundred years. The most notable example is probably the Minkowski...
متن کاملPrincipal Curvatures of Isoparametric Hypersurfaces in Cp
Let M be an isoparametric hypersurface in CPn, and M the inverse image of M under the Hopf map. By using the relationship between the eigenvalues of the shape operators of M and M , we prove that M is homogeneous if and only if either g or l is constant, where g is the number of distinct principal curvatures of M and l is the number of non-horizontal eigenspaces of the shape operator on M .
متن کاملThe curvatures of lightlike hypersurfaces of an indefinite Kenmotsu manifold
We study the forms of curvatures of lightlike hypersurfaces M of an indefinite Kenmotsu manifold M̄ subject to the conditions: (1) M is locally symmetric, i.e., the curvature tensor R of M be parallel on TM , or (2) M is a semi-symmetric manifold, i.e., R(X, Y )R = 0 on TM . M.S.C. 2010: 53C25, 53C40, 53C50.
متن کاملRigidity of minimal hypersurfaces of spheres with two principal curvatures
Let ν be a unit normal vector field along M . Notice that ν : M −→ S satisfies that 〈ν(m),m〉 = 0. For any tangent vector v ∈ TmM , m ∈ M , the shape operator A is given by A(v) = −∇̄vν, where ∇̄ denotes the Levi Civita connection in S. For every m ∈ M , A(m) defines a linear symmetric transformation from TmM to TmM ; the eigenvalues of this transformation are known as the principal curvatures of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1995
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500006283