WebKAHLER-EINSTEIN METRICS¨ 3 who generalized Futaki’s obstruction [93] to the notion of K-stability: Tian showed (see also Ding-Tian [65]) that given any C∗-equivariant family π : X → C with generic fiber Xt ∼= M, and Q-Fano central fiber X0, the Futaki invariant F(X) of the induced vector field on the central fiber can be defined. WebJul 20, 2024 · Using this result we calculate the generating function of the reduced Dirac and signature eta-invariants for the family of Berger metrics on the odd dimensional spheres. …
THE ETA INVARIANT IN THE DOUBLY KAHLERIAN¨ CONFORMALLY COMPACT EINSTEIN ...
WebJan 1, 1990 · This chapter focuses on homogeneous Einstein metrics on certain Kähler C -spaces. Most known nonstandard examples of compact homogeneous Einstein manifolds are constructed via Riemannian submersions. The word “standard” implies that the Einstein metric on a homogeneous manifold is constructed from the irreducible isotropy … WebThe $\rho $ -Einstein soliton is a self-similar solution of the Ricci–Bourguignon flow, which includes or relates to some famous geometric solitons, for example, the Ricci soliton and the Yamabe soliton, and so on.This paper deals with the study of $\rho $ -Einstein solitons on Sasakian manifolds.First, we prove that if a Sasakian manifold M admits a nontrivial … chris bell amarillo
THE ETA INVARIANT IN THE KAHLERIAN …
In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study. It may loosely be thought of as a generalization of the gravitational potential of Newtonian gravitation. The metric captures all the geometric and causal structure of spacetime, being used to define notions such as time, distance, volume, curvature, angle, and separation of the future and the past. WebInvariant Einstein metrics on $\mathrm{SU}(n)$ and complex Stiefel manifolds. Tohoku Mathematical Journal, Vol. 72, Issue. 2, CrossRef; Google Scholar; Arvanitoyeorgos, Andreas Sakane, Yusuke and Statha, Marina 2024. Homogeneous Einstein metrics on Stiefel manifolds associated to flag manifolds with two isotropy summands. Journal of … Webthe variational approach to the Einstein metrics is given in Proposition 4.5. In Sec-tion 5, as an application of our construction, we obtain Jensen’s invariant Einstein metrics on the Stiefel manifold SO(k1 + k2)/SO(k2). In Section 6 we investigate in-variant Einstein metrics on SO(sk + l)/SO(l). Finally, in Section 7 the proofs of the chris bellamy cohen