Results 31 to 40 of about 126 (113)
A classification of totally geodesic and totally umbilical Legendrian submanifolds of $$(\kappa ,\mu )$$ ( κ , μ ) -spaces [PDF]
Annals of Global Analysis and Geometry, 2018 We present classifications of totally geodesic and totally umbilical Legendrian submanifolds of $(κ,μ)$-spaces with Boeckx invariant $I \leq -1$. In particular, we prove that such submanifolds must be, up to local isometries, among the examples that we explicitly construct.
Alfonso Carriazo +2 more
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Radical Transversal Lightlike Submanifolds of Indefinite Para-Sasakian Manifolds
Demonstratio Mathematica, 2014 In this paper, we study radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds giving some non-trivial examples of these submanifolds.
Shukla S.S., Yadav Akhilesh
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Pseudo-totally umbilical lightlike submanifolds
Hacettepe Journal of Mathematics and Statistics, 2022 We introduce the geometry of pseudo-totally umbilical lightlike submanifold $M$ of a semi-Riemannian manifold $\bar{M}$. In line with the above, we give a complete classification of pseudo-totally umbilical $1$-lightlike submanifolds, such as the lightlike hypersurfaces and half-lightlike submanifolds.
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A Discrete Representation of the Second Fundamental Form
Mathematics, 2022 We present a new method to obtain a combinatorial representation for the behaviour of a submanifold isometrically immersed in a Riemannian manifold based on the second fundamental form.
Alfonso Carriazo +2 more
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Screen Cauchy–Riemann (SCR)-lightlike submanifolds of metallic semi-Riemannian manifolds [PDF]
Arab Journal of Mathematical SciencesPurposeThe screen Cauchy–Riemann (SCR)-lightlike submanifold is an important class of submanifolds of semi-Riemannian manifolds. It contains various other classes of submanifolds as its sub-cases. It has been studied under various ambient space.
Gauree Shanker +2 more
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On the three-dimensional CR-submanifolds of the six-dimensional sphere
International Journal of Mathematics and Mathematical Sciences, 1991 We show that the six-dimensional sphere does not admit three-dimensionel totally umbilical proper CR-submanifolds.
M. A. Bashir
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Isotropic Lagrangian Submanifolds in Complex Space Forms [PDF]
Journal of Sciences, Islamic Republic of Iran, 2012 In this paper we study isotropic Lagrangian submanifolds , in complex space forms . It is shown that they are either totally geodesic or minimal in the complex projective space , if . When , they are either totally geodesic or minimal in .
M.B. Kashani
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Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1656-1702, September 2025.Abstract Let (Mn,g)$(M^n,g)$ be a complete Riemannian manifold which is not isometric to Rn$\mathbb {R}^n$, has nonnegative Ricci curvature, Euclidean volume growth, and quadratic Riemann curvature decay. We prove that there exists a set G⊂(0,∞)$\mathcal {G}\subset (0,\infty)$ with density 1 at infinity such that for every V∈G$V\in \mathcal {G}$ there ...
Gioacchino Antonelli +2 more
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TOTALLY UMBILICAL CR-SUBMANIFOLDS OF A NEARLY KAEHLER MANIFOLD
Tamkang Journal of Mathematics, 1996 The geometry of a CR-submanifold in a Kaehler manifold has been extensively studied. B.Y . Chen has classified the totally umbilical CR-submanifolds of a Kaehler manifold and showed that they are either totally geodesic, or totally real or dim$(D^{\perp}) =1$. In this paper we show that such a result is also true in a nearly Kaehler manifold.
Kon, S. H., Tan, Sin-Leng
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On totally umbilical and minimal surfaces of the Lorentzian Heisenberg groups
Mathematische Nachrichten, Volume 298, Issue 6, Page 1922-1942, June 2025.Abstract This paper has manifold purposes. We first introduce a description of the Gauss map for submanifolds (both spacelike and timelike) of a Lorentzian ambient space and relate the conformality of the Gauss map of a surface to total umbilicity and minimality.
Giovanni Calvaruso +2 more
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