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Total Scalar Curvatures of Geodesic Spheres and of Boundaries of Geodesic Disks

2007
Total curvatures of boundaries of geodesic disks in Riemannian manifolds are investigated. The first terms in the corresponding power series expansions are obtained for the total scalar curvature and the L 2-norms of the scalar curvature, the Ricci tensor and the curvature tensor.
J. C. Díaz-Ramos, E. García-Río, L. Hervella +2 more
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The Totally Geodesic Coisotropic Submanifolds in Kähler Manifolds

Geometriae Dedicata, 2002
A real submanifold $\Sigma$ in a symplectic manifold $(M^{2n}, \omega)$ is said to be a coisotropic submanifold if $T_p\Sigma^\omega \subset T_p\Sigma$ for all $p\in\Sigma$, where $T_p\Sigma^\omega= \{X\in T_pM\mid \omega (X,Y)=0$, $\forall Y\subset T_p\Sigma\}$ is the symplectic complement of $T_p \Sigma$.
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Riemannian and Totally Geodesic Foliations

1988
The transversal geometry of a foliation is the geometry infinitesimally modeled by Q, while the tangential geometry is infinitesimally modeled by L. A key fact is the existence of the Bott connection in Q defined by $$ {\mathop{\nabla }\limits^{^\circ }_{{{X^S}}}} = \pi [X,{Y_S}]\,{\text{for}}\,X \in \Gamma L,\,s \in \Gamma Q $$ (5.1) where ...
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A Totally Real Surface in CP 2 that is not Totally Geodesic