Lie groups as 3-dimensional almost contact B-metric manifolds

Abstract

The object of investigations are almost contact B-metric structures on 3-dimensional Lie groups considered as smooth manifolds. There are established the existence and some geometric characteristics of these manifolds in all basic classes. An example is given as a support of obtained results.

arXiv comment13 pages

References in corpus (7)

• On Eta-Einstein Sasakian Geometry
• Natural connection with totally skew-symmetric torsion on almost contact manifolds with B-metric
• Sasaki-like almost contact complex Riemannian manifolds
• On the structure tensors of almost contact B-metric manifolds
• A classification of the torsion tensors on almost contact manifolds with B-metric
• Canonical-type connection on almost contact manifolds with B-metric
• Curvature properties on some classes of almost contact manifolds with B-metric

Cited by in corpus (11)

• Ricci-like solitons on almost contact B-metric manifolds
• Lie groups as 3-dimensional almost paracontact almost paracomplex Riemannian manifolds
• Matrix Lie groups as 3-dimensional almost contact B-metric manifolds
• On Geometry of Manifolds with Some Tensor Structures and Metrics of Norden Type
• Yamabe Solitons on Conformal Almost Contact Complex Riemannian Manifolds with Vertical Torse-Forming Vector Field
• Almost Riemann Solitons with Vertical Potential on Conformal Cosymplectic Contact Complex Riemannian Manifolds
• Lie groups as 3-dimensional almost contact B-metric manifolds in two main classes
• Pair of associated Schouten-van Kampen connections adapted to an almost paracontact almost paracomplex Riemannian structure
• Almost contact B-metric manifolds as extensions of a 2-dimensional space-form
• Lie groups as 3-dimensional almost contact B-metric manifolds in the main vertical classes
• Invariant tensors under the twin interchange of the pairs of the associated metrics on almost paracomplex pseudo-Riemannian manifolds