Riemann flow and Riemann wave via bialternate product Riemannian metric

Details Riemann flow and Riemann wave via bialternate product Riemannian metric Riemann flow and Riemann wave via bialternate product Riemannian metric

2011-12-19

arxiv.org/abs/1112.4279v3

Mathematics

Analysis of PDEs

16 pages

Scientific paper

We illustrate the flow or wave character of the metrics and curvatures of evolution manifolds, introducing the Riemann flow and the Riemann wave via the bialternate product Riemannian metric.This kind of evolutions are new and very natural to understand certain flow or wave phenomena in the nature as well as the geometry of manifolds. It possesses many interesting properties from both mathematical and physical point of views. We illustrate the novel features of Riemann flow and Riemann wave,as well as their versatility, by introducing new original results: (1) Riemann flow PDE and Riemann wave PDE, the meaning of the Riemann flows on constant curvature manifolds and the Riemann solitons, (2) the infinitesimal deformations (linearizations) of Ricci flow and of Riemann flow PDEs, (3) the existence of Ricci or Riemann curvature blow-up at finite-time singularities of the flow, the gradient Riemann soliton,(3) the Riemann waves and their meaning on constant curvature manifolds, (4) the existence of Ricci or Riemann curvature blow-up at finite-time singularities of the wave, (5) the general form of some essential PDE systems on Riemannian manifolds.

Affiliated with

Also associated with

No associations

Rating

Riemann flow and Riemann wave via bialternate product Riemannian metric does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Riemann flow and Riemann wave via bialternate product Riemannian metric, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Riemann flow and Riemann wave via bialternate product Riemannian metric will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-210436