Planar Pseudo-geodesics and Totally Umbilic Submanifolds. [PDF]
J Geom Anal, 2023 AbstractWe study totally umbilic isometric immersions between Riemannian manifolds. First, we provide a novel characterization of the totally umbilic isometric immersions with parallel normalized mean curvature vector, i.e., those having nonzero mean curvature vector and such that the unit vector in the direction of the mean curvature vector is ...
Markvorsen S, Raffaelli M.
europepmc +6 more sources
Curvature Invariants of Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature [PDF]
Entropy, 2018 In this article, we consider statistical submanifolds of Kenmotsu statistical manifolds of constant ϕ-sectional curvature. For such submanifold, we investigate curvature properties. We establish some inequalities involving the normalized δ-Casorati
Simona Decu +3 more
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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.
Luc Vrancken +2 more
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Arithmeticity, superrigidity, and totally geodesic submanifolds [PDF]
Annals of Mathematics, 2021 Corrected proof of folklore Proposition 3.1 and filled in minor omission in the proof of Lemma 3 ...
Bader, Uri +3 more
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Geometry of warped product pseudo slant submanifolds in nearly Lorentzian para Sasakian Manifold [PDF]
Journal of Hyperstructures, 2023 The object of the present paper is to study Lorentzian para-Sasakian manifold on a pseudo slant submanifold and usingsome properties like warped product on manifolds, totally geodesic foliation, integrability on the properties of nearly Lorentzian para ...
Shamsur Rahman, Avijit Kumar Paul
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A note on quasi-hemi slant submanifolds of nearly trans-Sasakian manifolds [PDF]
Journal of Hyperstructures, 2023 Here our main objective is to introduce the notion of quasi hemi-slant submanifolds as a generalized case of slant sub-manifolds, semi-slant submanifolds and hemi-slant submanifolds of contact metric manifolds.
Shamsur Rahman, Amit Kumar Rai
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Totally geodesic submanifolds of Teichmüller space [PDF]
Journal of Differential Geometry, 2020 We show that any totally geodesic submanifold of Teichmuller space of dimension greater than one covers a totally geodesic subvariety, and only finitely many totally geodesic subvarieties of dimension greater than one exist in each moduli space.
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Random Manifolds Have No Totally Geodesic Submanifolds [PDF]
Michigan Mathematical Journal, 2019 V2: minor changes to address referees' reports, calculations in the local construction have been made more explicit.
Murphy, Thomas, Wilhelm, Frederick
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Characterizations for totally geodesic submanifolds of a $ K $-paracontact manifold
AIMS Mathematics, 2021 The aim of the present paper is to study pseudoparallel invariant submanifolds of a K-paracontact metric manifold. We consider pseudoparallel, Ricci-generalized pseudoparallel and 2-Ricci generalized pseudo parallel invariant submanifolds of a K-paracontact manifold and we obtain new results.
Mert,Tuğba, Atçeken, Mehmet
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Rigidity of Complete Minimal Submanifolds in Spheres
Frontiers in Physics, 2020 Let M be an n-dimensional complete minimal submanifold in an (n + p)-dimensional sphere 𝕊n+p, and let h be the second fundamental form of M. In this paper, it is shown that M is totally geodesic if the L2 norm of |h| on any geodesic ball of M is of less ...
Jundong Zhou, Jundong Zhou
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