A functional expression for the curvature of hyper-dimensional Riemannian spaces.
This article deals with vector valued differential forms on -manifolds. As a generalization of the exterior product, we introduce an operator that combines -valued forms with -valued forms. We discuss the main properties of this operator such as (multi)linearity, associativity and its behavior under pullbacks, push-outs, exterior differentiation of forms, etc. Finally we present applications for Lie groups and fiber bundles.
In this paper, under the one-parameter closed planar homothetic motion, a generalization of Holditch Theorem is obtained by using two different line segments (with fixed lengths) whose endpoints move along two different closed curves.