Sasaki-like almost contact complex Riemannian manifolds

Abstract

A Sasaki-like almost contact complex Riemannian manifold is defined as an almost contact complex Riemannian manifold which complex cone is a holomorphic complex Riemannian manifold. Explicit compact and non-compact examples are given. A canonical construction producing a Sasaki-like almost contact complex Riemannian manifold from a holomorphic complex Riemannian manifold is presented and called an $S^1$-solvable extension.

19 pages

References in corpus (1)

• Holomorphic hypersurfaces of Kaehler manifolds with Norden metric

Cited by in corpus (12)

• Ricci-like solitons on almost contact B-metric manifolds
• Lie groups as 3-dimensional almost contact B-metric manifolds
• Ricci-like solitons with vertical potential on Sasaki-like almost contact B-metric manifolds
• On canonical-type connections on almost contact complex Riemannian manifolds
• Associated Nijenhuis Tensors on Manifolds with Almost Hypercomplex Structures and Metrics of Hermitian-Norden Type
• Yamabe solitons on conformal Sasaki-like 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
• Pairs of associated Yamabe almost solitons with vertical potential on almost contact complex Riemannian manifolds
• Natural Connections with Totally Skew-Symmetric Torsion on Manifolds with Almost Contact 3-Structure and Metrics of Hermitian-Norden Type
• Lie groups as 3-dimensional almost contact B-metric manifolds in the main vertical classes
• Almost contact B-metric manifolds as extensions of a 2-dimensional space-form