Using concepts from integral geometry, we propose a definition for local coarse-grained curvature tensor that is well-defined on polygonal surfaces. This shows fast convergence to the of smooth surfaces, capturing with accuracy not only principal curvatures but also directions curvature. Thanks additivity integrated tensor, coarse-graining procedures can be implemented compute it over arbitrary...

The object of the present paper is to study Z-symmetric manifold with projective curvature tensor. At first, we case Z-tensor and Ricci tensor being Codazzi type. Next, consider recurrent We also divergence-free Z-tensor. Finally, construct an example