On the geometry of the normal bundle with a metric of Cheeger-Gromoll type

2008/09/23 by Wojciech Kozłowski, Kozłowski, Wojciech
Mathematics · Physics and Astronomy · #53B35 #53C07 #53C25 #53C55 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0809.3884

openalex publication_date 2008/09/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/02

Abstract

We investigate the geometry of a normal bundle equipped with a (p,q)-metric, i.e., Riemannian metric of Cheeger-Gromoll type, to the submanifold of a Riemannian manifold. We derive all natural object as the Levi-Civita connection, curvature tensor, sectional and scalar curvature. We prove that under some natural conditions the sectional curvature of this bundle may be bounded from below by given arbitrary large positive constant. Next we investigate (p,q)-metrics from the complex geometry point of view. We show when the normal bundle can by equipped with a structure of almost Hermitian, almost Kählerian, conformally almost Kählerian or Kählerian manifold.

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