Invariant submanifolds of hyperbolic Sasakian manifolds and η-Ricci-Bourguignon solitons
Sudhakar Kumar Chaubey, Danish Siddiqi, D. G. Prakasha
Abstract
We set the goal to study the properties of invariant submanifolds of the hyperbolic Sasakian manifolds. It is proven that a three-dimensional submanifold of a hyperbolic Sasakian manifold is totally geodesic if and only if it is invariant. Also, we discuss the properties of ?-Ricci-Bourguignon solitons on invariant submanifolds of the hyperbolic Sasakian manifolds. Finally, we construct a non-trivial example of a three-dimensional invariant submanifold of five-dimensional hyperbolic Sasakian manifold and validate some of our results.
Topics & Concepts
SubmanifoldMathematicsInvariant (physics)Hyperbolic manifoldHyperbolic 3-manifoldPure mathematicsMathematical analysisTotally geodesicManifold (fluid mechanics)Stable manifoldRelatively hyperbolic groupHyperbolic functionMathematical physicsEngineeringMechanical engineeringGeometric Analysis and Curvature FlowsGeometry and complex manifoldsGeometric and Algebraic Topology