Results 51 to 60 of about 18,512 (114)

ON TOTALLY UMBILICAL SUBMANIFOLDS OF SOME CLASS RIEMANNIAN MANIFOLDS

Demonstratio Mathematica, 1983
The authors study totally umbilical submanifolds M with parallel mean curvature vector in pseudo-Riemannian manifolds N, such that the curvature tensor R of M satisfies \(R(X,Y)\cdot R=0\), while N carries a generalized curvature tensor \(\tilde T\) with \(\tilde R\)(X,Y)\(\cdot \tilde T=0\), \(\tilde R\) being the curvature of N.
Adamów, Adam, Deszcz, Ryszard
openaire   +2 more sources

Totally Umbilical Screen Transversal Lightlike Submanifolds of Semi-Riemannian Product Manifolds

, 2012
We study totally umbilical screen transversal lightlike submanifolds immersed in a semi-Riemannian product manifold and obtain necessary and sufficient conditions for induced connection ▽ on a totally umbilical radical screen transversal lightlike ...
S. Haider, Advin Maseih, M. Thakur
semanticscholar   +1 more source

The Morse Index of Sacks–Uhlenbeck α‐Harmonic Maps for Riemannian Manifolds

Journal of Mathematics, Volume 2024, Issue 1, 2024.
In this paper, first we prove a nonexistence theorem for α‐harmonic mappings between Riemannian manifolds. Second, the instability of nonconstant α‐harmonic maps is studied with regard to the Ricci curvature criterion of their codomain. Then, we estimate the Morse index for measuring the degree of instability of some particular α‐harmonic maps ...
Amir Shahnavaz, Nader Kouhestani, Seyed Mehdi Kazemi Torbaghan, Antonio Masiello   +3 more
wiley   +1 more source

Time‐Dependent Evolving Null Horizons of a Dynamical Spacetime

International Scholarly Research Notices, Volume 2014, Issue 1, 2014., 2014
Totally geodesic null hypersurfaces have been widely used in the study of isolated black holes. In this paper, we introduce a new quasilocal notion of a family of totally umbilical null hypersurfaces called evolving null horizons (ENH) of a dynamical spacetime, satisfied under an appropriate energy condition.
K. L. Duggal, U. Kulshreshtha, W.-H. Steeb   +2 more
wiley   +1 more source

CR-hypersurfaces of the six-dimensional sphere

International Journal of Mathematics and Mathematical Sciences, 1994
We proved that there does not exist a proper CR-hypersurface of S6 with parallel second fundamental form. As a result of this we showed that S6 does not admit a proper CR-totally umbilical hypersurface.
M. A. Bashir
doaj   +1 more source

A characterisation of Riemannian foliations and totally umbilical submanifolds [PDF]

Bulletin of the Australian Mathematical Society, 1993
We discuss characterisations of Riemannian foliations, totally geodesic submanifolds, and totally umbilical submanifolds by sharp inequalities. These derive from the same linear algebraic set up, characterising a linear endomorphism which is a multiple of the identity.
Tondeur, Ph., Vanhecke, L.
openaire   +2 more sources

New Characterizations of Hyperspheres and Spherical Hypercylinders in Euclidean Space

Journal of Mathematics, Volume 2024, Issue 1, 2024.
Let x be an isometric immersion of a Riemannian n‐manifold M into a Euclidean (n + 1)‐space En+1 which does not pass through the origin of En+1. Then, the tangential part of the position vector field x of x is called the canonical vector field, and the normal part gives rise to a scalar function called the support function.
Nasser Bin Turki, Sharief Deshmukh, Bang-Yen Chen, Ljubisa Kocinac   +3 more
wiley   +1 more source

Study of bi-f-harmonic curve along immersions

Miskolc Mathematical Notes
In this paper, we characterize the bi-f-harmonic curve on surfaces and then we study the submanifold of a Riemannian manifold using the bi-f-harmonic curve.
Buddhadev Pal, Mahendra Kumar, Santosh Kumar   +2 more
doaj   +1 more source

On totally umbilical QR-submanifolds of quaternion Kaehlerian manifolds

Bulletin of the Australian Mathematical Society, 2000
We introduce the notion of generalised 3-Sasakian structure on a manifold and show that a totally umbilical, but not totally geodesic, proper QR-submanifold of a quaternion Kaehlerian manifold is an extrinsic sphere and inherits such a structure.
A. Bejancu, H. Farran
semanticscholar   +1 more source

On Surfaces of Exceptional Lorentzian Lie Groups with a Four-Dimensional Isometry Group

Mathematics
In total, geodesic surfaces and their generalizations, namely totally umbilical and parallel surfaces, are well-known topics in Submanifold Theory and have been intensively studied in three-dimensional ambient spaces, both Riemannian and Lorentzian.
Giovanni Calvaruso, Lorenzo Pellegrino
doaj   +1 more source