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On Totally Geodesic Submanifolds
AxiomsWe give a proof of Cartan’s Theorem on totally geodesic submanifolds for real analytic manifolds endowed with a real analytic, torsion-free, affine connection. We apply the theorem to real analytic Hadamard manifolds and, more generally, to real analytic
Antonella Nannicini, Donato Pertici
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Homogeneous hypersurfaces and totally geodesic submanifolds [PDF]
, 2022 This Ph.D. thesis deals with the study of certain classes of submanifolds in the presence of symmetry. Namely, results have been derived regarding the theory of submanifolds in Riemannian homogeneous spaces with a special emphasis on symmetric spaces.
Rodríguez Vázquez, Alberto
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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.
Alfonso Carriazo +2 more
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Totally geodesic submanifolds in exceptional symmetric spaces
Advances in Mathematics, 2023 We classify maximal totally geodesic submanifolds in exceptional symmetric spaces up to isometry. Moreover, we introduce an invariant for certain totally geodesic embeddings of semisimple symmetric spaces, which we call the Dynkin index. We prove a result analogous to the index conjecture: for every irreducible symmetric space of non-compact type ...
Kollross, Andreas +1 more
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Minimality of totally geodesic submanifolds in Finsler geometry [PDF]
Mathematische Annalen, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Berck, Gautier
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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.
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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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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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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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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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