Results 41 to 50 of about 126 (113)
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
Multiplicative rectifying submanifolds of multiplicative Euclidean space
Mathematical Methods in the Applied Sciences, Volume 48, Issue 1, Page 329-339, 15 January 2025.In this paper, we initiate the study of the multiplicative Euclidean submanifolds, exhibiting the multiplicative counterparts of the Gauss–Weingarten formulas. Some particular types such as multiplicative conic, spherical, and totally geodesic submanifolds are analyzed.
Muhittin Evren Aydin +2 more
wiley +1 more source
Totally umbilical CR-submanifolds of a Kaehler manifold [PDF]
Kodai Mathematical Journal, 1986 It was proved [see the reviewer, Geometry of CR-submanifolds (1986; Zbl 0605.53001); Theorem 2.1, p. 43] that a totally umbilical CR-submanifold M of a Kaehler manifold N is either totally geodesic or totally real, or dim \(D^{\perp}=1\). In the last case, \textit{T. Toyonari} and \textit{H. Nemoto} [TRU Math.
Deshmukh, Sharief, Husain, S. I.
openaire +3 more sources
Constrained deformations of positive scalar curvature metrics, II
Communications on Pure and Applied Mathematics, Volume 77, Issue 1, Page 795-862, January 2024.Abstract We prove that various spaces of constrained positive scalar curvature metrics on compact three‐manifolds with boundary, when not empty, are contractible. The constraints we mostly focus on are given in terms of local conditions on the mean curvature of the boundary, and our treatment includes both the mean‐convex and the minimal case.
Alessandro Carlotto, Chao Li
wiley +1 more source
Lightlike Hypersurfaces of Indefinite Generalized Sasakian Space Forms
Journal of Applied Mathematics, Volume 2015, Issue 1, 2015., 2015 We study lightlike hypersurfaces M of an indefinite generalized Sasakian space form M-(f1,f2,f3), with indefinite trans‐Sasakian structure of type (α, β), subject to the condition that the structure vector field of M- is tangent to M. First we study the general theory for lightlike hypersurfaces of indefinite trans‐Sasakian manifold of type (α, β ...
Dae Ho Jin, Dimitris Fotakis
wiley +1 more source
Totally umbilical submanifolds in irreducible symmetric spaces [PDF]
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1982 AbstractA submanifold of a Riemannian manifold is called a totally umbilical submanifold if its first and second fundamental forms are proportional. In this paper we prove the following best possible result.
Chen, Bang-Yen, Verheyen, Paul
openaire +2 more sources
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 +3 more
wiley +1 more source
Pseudo-Slant submaniolds of nearly δ- Lorentzian trans Sasakian manifolds [PDF]
Journal of HyperstructuresOur focus is on the existence of certain structures and similarities between pseudo slant submanifolds and nearly δ- Lorentzian trans Sasakian manifolds.
Shamsur Rahman
doaj +1 more source
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 +3 more
wiley +1 more source
Totally umbilical proper slant submanifolds of para-Kenmotsu manifold
Cubo, 2019 In this paper, we study slant submanifolds of a para-Kenmotsu manifold. We prove that totally umbilical slant submanifold of a para-Kenmotsu manifold is either invariant or anti-invariant or dimension of submanifold is 1 or the mean curvature vector H of
M.S. Siddesha, C.S. Bagewadi, D. Nirmala
doaj +1 more source