Isometric immersions into manifolds with metallic structures [PDF]
arXiv, 2017 We consider submanifolds into Riemannian manifold with metallic structures. We obtain some new results for hypersurfaces in these spaces and we express the fundamental theorem of submanifolds into products spaces in terms of metallic structures. Moreover, we define new structures called complex metallic structures.
arxiv
Sub-Riemannian geometry and Lie groups. Part II. Curvature of metric spaces, coadjoint orbits and associated representations [PDF]
arXiv, 2004 This paper is the third in a series dedicated to the fundamentals of sub-Riemannian geometry and its implications in Lie groups theory: "Sub-Riemannian geometry and Lie groups. Part I", math.MG/0210189, available at http://arxiv.org/abs/math.MG/0210189, and "Tangent bundles to sub-Riemannian groups", math.MG/0307342, available at http://arxiv.org/abs ...
arxiv
A Schur-Toponogov theorem in Riemannian geometry & a new proof of Toponogov's theorem in Alexandrov geometry [PDF]
arXiv, 2018 In the paper, we give a Schur-Toponogov theorem in Riemannian geometry, which not only generalizes Schur's and Toponogov's theorem but also indicates their relation. Inspired by its proof, we also supply a new proof of Toponogov's theorem (in the large) in Alexandrov geometry.
arxiv
A fundamental theorem for submanifolds in semi-Riemannian warped products [PDF]
Journal of Geometry and Physics, 2017 Carlos A. D. Ribeiro, Marcos F. de Melo
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A duality theorem for Riemannian foliations in nonnegative sectional curvature [PDF]
arXiv, 2006 Using a new type of Jacobi field estimate we will prove a duality theorem for singular Riemannian foliations in complete manifolds of nonnegative sectional curvature.
arxiv
A decomposition theorem for immersions of product manifolds [PDF]
arXiv, 2013 We introduce polar metrics on a product manifold, which have product and warped product metrics as special cases. We prove a de Rham-type theorem characterizing Riemannian manifolds that can be locally decomposed as a product manifold endowed with a polar metric.
arxiv
Anti-invariant Riemannian submersions from locally conformal Kaehler manifolds [PDF]
arXiv, 2019 B. Sahin [9] introduced the notion of anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. In the present paper we extend the notion of anti-invariant and Lagrangian Riemannian submersions (a special anti-invariant Riemannian submersion) to the case of locally conformal Kaehler manifolds.
arxiv
A Bonnet-Myers type theorem for quaternionic contact structures [PDF]
arXiv, 2017 We prove a Bonnet-Myers type theorem for quaternionic contact manifolds of dimension bigger than 7. If the manifold is complete with respect to the natural sub-Riemannian distance and satisfies a natural Ricci-type bound expressed in terms of derivatives up to the third order of the fundamental tensors, then the manifold is compact and we give a sharp ...
arxiv
A Note on the Geometry of Positively-Curved Riemannian Manifolds [PDF]
arXiv, 2013 In this paper I present a comparison theorem for the waist of Riemannian manifolds with positive sectional curvature. The main theorem of this paper gives a partial positive answer to a conjecture formulated by M.Gromov in [8]. The content of this paper combines two aspects: classical volume comparison theorems of Riemannian geometry, and geometric ...
arxiv
Some semi-Riemannian volume comparison theorems [PDF]
Tohoku Math. J. 52 (2000) 331-348, 1998 Lorentzian versions of classical Riemannian volume comparison theorems by Gunther, Bishop and Bishop-Gromov, are stated for suitable natural subsets of general semi-Riemannian manifolds. The problem is more subtle in the Bishop-Gromov case, which is extensively discussed.
arxiv