Deformations of structures, embedding of a Riemannian manifold in a Kählerian one and geometric antigravitation

• Autorzy: Alexander A. Ermolitski
• Języki publikacji: EN

Abstrakty

EN

Tubular neighborhoods play an important role in modern differential topology. The main aim of the paper is to apply these constructions to geometry of structures on Riemannian manifolds. Deformations of tensor structures on a normal tubular neighborhood of a submanifold in a Riemannian manifold are considered in section 1. In section 2, this approach is used to obtain a Kählerian structure on the corresponding normal tubular neighborhood of the null section in the tangent bundle TM of a smooth manifold M. In section 3, we consider a new deformation of a tensor structure on some neighborhood of a curve and introduce the so-called geometric antigravitation. Some results of the paper were announced in [4], [5]. The work [3] is close to our discussion.

Kategorie tematyczne

• 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions
• 53C26: Hyper-K\"ahler and quaternionic K\"ahler geometry, ``special'' geometry
• 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2007
• Tom: 76
• Numer: 1
• Strony: 505-514

Daty

wydano

2007

Twórcy

autor

Alexander A. Ermolitski

• Chair of Mathematics, Belorussian State Pedagogical University, Sovietskaya 18, Minsk 220050, Belarus

Identyfikatory

DOI

10.4064/bc76-0-26