Isometric immersions of Riemannian manifolds

@article{Omori1967IsometricIO,
  title={Isometric immersions of Riemannian manifolds},
  author={Hideki. Omori},
  journal={Journal of The Mathematical Society of Japan},
  year={1967},
  volume={19},
  pages={205-214}
}
  • Hideki. Omori
  • Published 1 April 1967
  • Mathematics
  • Journal of The Mathematical Society of Japan
View via Publisher
projecteuclid.org
299 Citations
Highly Influential Citations
37
Background Citations
60
Methods Citations
68
Results Citations
2

299 Citations

Generalized Maximum Principles and Stochastic Completeness for Pseudo-Hermitian Manifolds

In this paper, the authors establish a generalized maximum principle for pseudo-Hermitian manifolds. As corollaries, Omori-Yau type maximum principles for pseudo-Hermitian manifolds are deduced.…

New Calabi–Bernstein type results in weighted generalized Robertson–Walker spacetimes

We apply suitable generalized maximum principles in order to obtain new Calabi–Bernstein’s type results concerning complete spacelike hypersurfaces immersed in a weighted generalized Robertson–Walker…

Topology and geometry of complete submanifolds in euclidean spaces

This paper is a survey of results on topological structures and curvature structures of complete submanifolds in a Euclidean space.

Semi-Kaehlerian submanifolds of an indefinite complex space form

The purpose of this paper is to study several classes of semi-Kaehlerian submanifolds of an indefinite complex space form. Introduction. An indefinite Kaehlerian manifold of constant holomorphic…

Spacelike translating solitons of the mean curvature flow in Lorentzian product spaces with density

By applying suitable Liouville-type results, an appropriate parabolicity criterion, and a version of the Omori-Yau's maximum principle for the drift Laplacian, we infer the uniqueness and…

Uniqueness and nonexistence of complete spacelike hypersurfaces, Calabi–Bernstein type results and applications to Einstein–de Sitter and steady state type spacetimes

We investigate the geometry of complete spacelike hypersurfaces (immersed) in a generalized Robertson-Walker spacetime -I×fMn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}…

Characterizations of complete linear Weingarten spacelike submanifolds in a locally symmetric semi-Riemannian manifold

The first author is partially supported by CAPES, Brazil. The second author is partially supported by CNPq, Brazil, grant 303977/2015- 9. The fourth author is partially supported by CNPq, Brazil,…

Geometric properties of the space of Lagrangian self-shrinking tori in ℝ⁴

We prove that any sequence {Fn : Σ→ R4} of conformally branched compact Lagrangian self-shrinkers to the mean curvature flow with uniform area upper bound has a convergent subsequence, if the…

A gap theorem for complete space-like hypersurface with constant scalar curvature in locally symmetric Lorentz spaces

Let M n be a complete space-like hypersurface with constant scalar curvature in locally symmetric Lorentz space N n+1 1 , S be the squared norm of the second fundamental form of M n in N n+1 1 .I n…

WITH ZERO GAUSS-KRONECKER CURVATURE

In this paper, we study complete maximal space-like hypersurfaces with constant Gauss-Kronecker curvature in an anti- de Sitter space H 4(i1). It is proved that complete maximal space- like…
...

References

Manifolds with positive curvature