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Slant lightlike submanifolds of indefinite Kenmotsu manifolds
Degenerate metric Slant lightlike submanifolds Kenmotsu manifold
2011/4/6
In this paper, we introduce the notion of a slant lightlike submanifold of an indefinite Kenmotsu manifold. We provide a non-trivial example and obtain necessary and sufficient conditions for the exis...
Embeddedness of proper minimal submanifolds in homogeneous spaces
minimal submanifolds homogeneous spaces
2010/11/23
We prove the three embeddedness results as follows. $({\rm i})$ Let $\Gamma_{2m+1}$ be a piecewise geodesic Jordan curve with $2m+1$ vertices in $\mathbb{R}^n$, where $m$ is an integer $\geq2$. Then t...
A symmetry result on submanifolds of space forms and Applications
submanifolds space forms Applications
2010/11/11
In this paper we prove a symmetry result on submanifolds of codimension one in a n + 1-dimensional space form, related to the geodesic distance function and to the normal curvature of some fixed vect...
A General Optimal Inequality for Arbitrary Riemannian Submanifolds
$delta$-invariants Inequality Riemannian submanifold Squared mean curvature Sectional curvature
2008/7/3
One of the most fundamental problems in submanifold theory is to establish simple relationships between intrinsic and extrinsic invariants of the submanifolds (cf. [6]). A general optimal inequality f...