1. CMB 2011 (vol 56 pp. 173)
|Semi-invariant Submersions from Almost Hermitian Manifolds|
We introduce semi-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations that arise from the definition of a Riemannian submersion, and find necessary sufficient conditions for total manifold to be a locally product Riemannian manifold. We also find necessary and sufficient conditions for a semi-invariant submersion to be totally geodesic. Moreover, we obtain a classification for semi-invariant submersions with totally umbilical fibers and show that such submersions put some restrictions on total manifolds.
Keywords:Riemannian submersion, Hermitian manifold, anti-invariant Riemannian submersion, semi-invariant submersion
2. CMB 2008 (vol 51 pp. 359)
|Real Hypersurfaces in Complex Space Forms with Reeb Flow Symmetric Structure Jacobi Operator |
Real hypersurfaces in a complex space form whose structure Jacobi operator is symmetric along the Reeb flow are studied. Among them, homogeneous real hypersurfaces of type $(A)$ in a complex projective or hyperbolic space are characterized as those whose structure Jacobi operator commutes with the shape operator.
Keywords:complex space form, real hypersurface, structure Jacobi operator
Categories:53B20, 53C15, 53C25
3. CMB 2002 (vol 45 pp. 161)
|Sur les singularitÃ©s de la fonction croissance d'une variÃ©tÃ© non simplement connexe |
Si $M$ est une vari\'et\'e de dimension $n$, compacte non simplement connexe, on caract\'erise les m\'etriques riemanniennes sur $M$ dont la fonction croissance a exactement deux singularit\'es.
Keywords:fonction croissance, singularitÃ©s, fonction de Morse, Cutlocus