Curvature Tensor under the Yamabe Flow

Jing Fang Shen; Jia Jun Yang; Neng Xi

doi:10.4028/www.scientific.net/AMR.459.514

Paper Titles

Spectral Analysis for Temporal and Spatial Variability of AF Signal
p.496

The Influences of Travel Product Types on Online Travel Purchasing of e-Travel Agency
p.500

Optimal Guidance Law Design for Reentry Vehicles with Terminal Velocity and Angle Constraints
p.505

The Embedded Quality Control System of Product Manufacturing Process
p.510

Curvature Tensor under the Yamabe Flow
p.514

Acoustic Feature-Based Clustering Analysis for Phonetic Degree of Chinese Phonogram
p.518

On General Scheme of Railway Bureau Emergency Command System
p.523

Underwater Electromagnetic Sources 2-D DOA and Polarization Estimation
p.529

Simulation Research on Direct 3D ECT Imaging Based on 16 Electrodes
p.535

HomeAdvanced Materials ResearchAdvanced Materials Research Vol. 459Curvature Tensor under the Yamabe Flow

Curvature Tensor under the Yamabe Flow

Abstract:

Yamabe flow, curvature, tensor, compact. Abstract. This paper focuses a compact Riemannian manifold Mn evolving under the Yamabe flow and proves that if the Ricci curvature is uniformly bounded under the flow for all times that t from 0 to T and the injectivity radius is bounded below at each time slice, then the curvature tensor is uniformly bounded.

You might also be interested in these eBooks

View Preview

Info:

Periodical:

Advanced Materials Research (Volume 459)

Pages:

514-517

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.459.514

Citation:

Cite this paper

Online since:

January 2012

Authors:

Jing Fang Shen, Jia Jun Yang, Neng Xi

Keywords:

Compact, Curvature, Tensor, Yamabe Flow

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

References

[1] B. Chow, The Yamabe Flow on Locally Conformally Flat Manifolds with Positive Ricci Curvature. Comm. Pure Appl. Math. vol. XLV, pp.1003-1014, (1992).

DOI: 10.1002/cpa.3160450805

Google Scholar

[2] R.G. Ye, Global Existence and Convergence of Yamabe Flow. J. Diff. Geom. vol 39, 35-50, (1994).

Google Scholar

[3] N. Sesum, Curvature Tensor under the Ricci flow. arXiv: math/0311397v2[math. DG].

Google Scholar

[4] G. Perelman, The Entropy Formula for the Ricci Flow and its Geometric Applications, http: /arxiv. org/abs/math/0211159.

Google Scholar

[5] H.L. Gu, Manifolds with Pointwise Ricci Pinched Curvature, arXiv: 0707. 0034v1 [math. DG].

Google Scholar

[6] D. Glickenstein, Precompactness of solutions to the Ricci flow in the absence of injectivity radius estimates, Geometry and Topology, 487C510, (2003).

DOI: 10.2140/gt.2003.7.487

Google Scholar

[7] R. Hamilton, A Compactness Property for Solutions of the Ricci flow, Amer.J. Math., vol 117, 545-572, (1995).

Google Scholar

[8] B. Chow,P. Lu,L. Ni, Hamilton's Ricci Flow, Lectures in Contemporary Mathematics 3. (2005).

Google Scholar

[9] H.D. Cao, X.P. Zhu, A Complete Proof of the Poincare and Geometrization Conjectures-Application of the Hamilton-Perelman Theory of the Ricci Flow. Asian J. Math. Vol 10, No 2, pp.165-492, 2006. 7.

DOI: 10.4310/ajm.2006.v10.n2.a2

Google Scholar

[10] B. Kleiner, J. Lott, Notes on Perelman's papers, arXiv: math/0605667v3[math. DG].

Google Scholar