Inequalities for the Casorati Curvature of Totally Real Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms. [PDF]
Entropy (Basel), 2021 Chen BY, Decu S, Vîlcu GE.
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Geometric characterization of totally geodesic SODE submanifolds
, 2019 Investigating the geometry of the tangent bundle (TMM) over a smooth manifold M is one of the most significant fields of modern differential geometry and has remarkable applications in various problems specifically in the theory of physical fields.
Muhammad Nizammul Hayad Bin Yahya
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Benjamini-Schramm convergence of periodic orbits. [PDF]
Geom Dedic, 2022 Mohammadi A, Rafi K.
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Casorati Inequalities for Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature with Semi-Symmetric Metric Connection. [PDF]
Entropy (Basel), 2022 Decu S, Vîlcu GE.
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Totally geodesic submanifolds of regular Sasakian manifolds
Osaka Journal of Mathematics, 2012 The main result of this paper finds a correspondence between certain types of totally geodesic submanifolds of a homogeneous Sasakian manifold (necessarily regular) and submanifolds of its Hermitian symmetric base space (via the Boothby-Wang fibration).
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Positively curved totally real minimal submanifolds immersed in a complex projective space
, 1976 A sufficient condition for a complete totally real minimal submanifold immersed in a complex projective space to be totally geodesic is given in terms of sectional curvature.
Koichi Ogiue
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A Riemannian Geometry Theory of Synergy Selection for Visually-Guided Movement. [PDF]
Vision (Basel), 2021 Neilson PD, Neilson MD, Bye RT.
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Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups
, 2007 We give a complete list of left-invariant unit vector fields on three-dimensional Lie groups equipped with a left-invariant metric that generate a totally geodesic submanifold in the unit tangent bundle of a group equipped with the Sasaki metric.
Yampolsky, A.
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On Ricci curvature of totally real submanifolds in a quaternion projective space [PDF]
, 2002 summary:Let $M^n$ be a Riemannian $n$-manifold. Denote by $S(p)$ and $\overline{\operatorname{Ric}}(p)$ the Ricci tensor and the maximum Ricci curvature on $M^n$, respectively.
Liu, Ximin
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Symplectomorphic codimension 1 totally geodesic submanifolds
Differential Geometry and its Applications, 1995 We show that the coisotropic totally geodesic properly embedded submanifolds of codimension 1 of a simply connected complete Kähler manifold of non-positive sectional curvature are symplectically linearizable. First we show that such a submanifold is foliated by totally geodesic complex leaves transversal to an isometric flow, hence, by a result of E ...
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