Einstein metrics and Ricci solitons

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imported>Pythagoras0님의 2015년 12월 25일 (금) 02:37 판
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introduction

  • A Riemannian manifold $(M, g)$ is called Einstein if it has constant Ricci curvature, i.e. $Ric_g=\lambda\cdot g$ for some $\lambda\in \mathbb{R}$
  • Einstein manifolds, conformal Einstein manifolds and (generic and gradient) Ricci solitons
  • Ricci solitons on Finsler spaces, previously developed by the present authors, are a generalization of Einstein spaces, which can be considered as a solution to the Ricci flow on compact Finsler manifolds.


books


expositions


articles

  • Arvanitoyeorgos, Andreas, Yusuke Sakane, and Marina Statha. “New Einstein Metrics on the Lie Group $SO(n)$ Which Are Not Naturally Reductive.” arXiv:1511.08849 [math], November 25, 2015. http://arxiv.org/abs/1511.08849.
  • Stolarski, Maxwell. “Steady Ricci Solitons on Complex Line Bundles.” arXiv:1511.04087 [math], November 12, 2015. http://arxiv.org/abs/1511.04087.
  • Bidabad, Behroz, and Mohamad Yar Ahmadi. “On Compact Ricci Solitons in Finsler Geometry.” arXiv:1508.02148 [math], August 10, 2015. http://arxiv.org/abs/1508.02148.
  • Nurowski, Pawel, and Matthew Randall. “Generalised Ricci Solitons.” arXiv:1409.4179 [gr-Qc], September 15, 2014. http://arxiv.org/abs/1409.4179.
  • Fernandez-Lopez, Manuel, and Eduardo Garcia-Rio. “On Gradient Ricci Solitons with Constant Scalar Curvature.” arXiv:1409.3359 [math], September 11, 2014. http://arxiv.org/abs/1409.3359.
  • Catino, Giovanni, Paolo Mastrolia, Dario D. Monticelli, and Marco Rigoli. 2014. “Conformal Ricci Solitons and Related Integrability Conditions.” arXiv:1405.3169 [math], May. http://arxiv.org/abs/1405.3169.