Positive curvature, like that on a sphere, implies a finite universe, while zero curvature, as on a flat plane or negative ...

General Relativity reinterprets the force of gravity not as a traditional force but as a manifestation of the curvature of spacetime. Its formulation rests on a rigorous mathematical framework built ...

In this paper, we introduce a new type of curvature tensor named 𝓗-curvature tensor of type (1, 3) which is a linear combination of conformal and projective curvature tensors. First we deduce some ...

Riemannian manifolds or geodesic metric spaces of finite or infinite dimension occur in many areas of mathematics. We are interested in the interplay between their local geometry and global ...

Biharmonic maps extend the concept of harmonic maps by exploring critical points of higher order energy functionals. In Riemannian geometry, while harmonic maps minimise the classical energy ...