Ricci decomposition

About: Ricci decomposition is a research topic. Over the lifetime, 1972 publications have been published within this topic receiving 45295 citations.

On Recurrent Riemannian Manifolds

Abstract: Recurrent spaces have been of great interest and were studied by a large number of authors such as Ruse ([3]), Patterson ([2]), Singh and Khan ([4], [5]) etc. In this paper, I have discussed the nature of 1-form for non-zero constant scalar curvature and non-constant scalar curvature r in a Ricci recurrent Riemannian manifold. I have obtained some results for conharmonic curvature tensor and also investigated some results for (1, 3) type tensors in a Riemannian manifold.

A Class of Lorentzian α-Sasakian Manifolds

Abstract: In this study we consider φ conformally at, φ conharmonically at, φ projectively at and φ concircularly at Lorentzian α Sasakian manifolds. In all cases, we get the manifold will be an η Einstein manifold.

How to produce a Ricci Flow via Cheeger-Gromoll exhaustion

Abstract: We prove short time existence for the Ricci flow on open manifolds of nonnegative complex sectional curvature We do not require upper curvature bounds By considering the doubling of convex sets contained in a Cheeger-Gromoll convex exhaustion and solving the singular initial value problem for the Ricci flow on these closed manifolds, we obtain a sequence of closed solutions of the Ricci flow with nonnegative complex sectional curvature which subconverge to a solution of the Ricci flow on the open manifold Furthermore, we find an optimal volume growth condition which guarantees long time existence, and we give an analysis of the long time behaviour of the Ricci flow Finally, we construct an explicit example of an immortal nonnegatively curved solution of the Ricci flow with unbounded curvature for all time

On Conformally at Almost Pseudo Ricci Symmetric Mani-folds

Abstract: The object of the present paper is to study conformally at almost pseudo Ricci symmetric manifolds. The existence of a conformally at almost pseudo Ricci symmetric manifold with non-zero and non-constant scalar curvature is shown by a non-trivial example. We also show the existence of an n-dimensional non-conformally at almost pseudo Ricci symmetric manifold with vanishing scalar curvature.

Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold

Abstract: Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on degenerate tensors which form curves. In this paper, we introduce a number of feature surfaces, such as neutral surfaces and traceless surfaces , into tensor field analysis, based on the notion of eigenvalue manifold . Neutral surfaces are the boundary between linear tensors and planar tensors, and the traceless surfaces are the boundary between tensors of positive traces and those of negative traces. Degenerate curves, neutral surfaces, and traceless surfaces together form a partition of the eigenvalue manifold, which provides a more complete tensor field analysis than degenerate curves alone. We also extract and visualize the isosurfaces of tensor modes, tensor isotropy, and tensor magnitude, which we have found useful for domain applications in fluid and solid mechanics. Extracting neutral and traceless surfaces using the Marching Tetrahedra method can cause the loss of geometric and topological details, which can lead to false physical interpretation. To robustly extract neutral surfaces and traceless surfaces, we develop a polynomial description of them which enables us to borrow techniques from algebraic surface extraction, a topic well-researched by the computer-aided design (CAD) community as well as the algebraic geometry community. In addition, we adapt the surface extraction technique, called A-patches , to improve the speed of finding degenerate curves. Finally, we apply our analysis to data from solid and fluid mechanics as well as scalar field analysis.