We construct an algebra of nonlinear generalized tensor fields on manifolds in the sense of Colombeau, i.e., containing distributional tensor fields as a linear subspace and smooth tensor fields as a ...

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 ...

The geometry of spacetime forms the very foundation of modern gravitational theory, where the elegant interplay between curvature and matter is described by Einstein’s field equations. In this ...

Riemannian geometry provides the essential framework for analysing curved spaces by endowing manifolds with a smoothly varying metric. This field has enabled statisticians to extend classical ...