Engineering

Curvature

Riemann curvature tensor

Pure mathematics

Fundamental theorem of Riemannian geometry

Ricci curvature

Economics

Mechanical engineering

Tangent space

Mathematics

Mathematical analysis

Operations management

Geometry

Connection (principal bundle)

Tangent bundle

Combinatorics

Metric connection

Normal bundle

Vector bundle

Levi-Civita connection

Metric (unit)

Topology (electrical circuits)

Manifold (fluid mechanics)

Unit tangent bundle

The objective of this paper is to explore the complete lifts of a quarter-symmetric metric connection from a Sasakian manifold to its tangent bundle. A relationship between the Riemannian connection and the quarter-symmetric metric connection from a Sasakian manifold to its tangent bundle was established. Some theorems on the curvature tensor and the projective curvature tensor of a Sasakian manifold with respect to the quarter-symmetric metric connection to its tangent bundle were proved. Finally, locally ϕ-symmetric Sasakian manifolds with respect to the quarter-symmetric metric connection to its tangent bundle were studied.

Lifts of a Quarter-Symmetric Metric Connection from a Sasakian Manifold to Its Tangent Bundle