Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn vector bundle manifolds with spherically symmetric metrics
169
0
0.0
(
0
)
Authors
Rui Albuquerque
Ask ChatGPT about the research
No Arabic abstract
We give a general description of the construction of weighted spherically symmetric metrics on vector bundle manifolds, i.e. the total space of a vector bundle $Erightarrow M$, over a Riemannian manifold $M$, when $E$ is endowed with a metric connection. The tangent bundle of $E$ admits a canonical decomposition and thus it is possible to define an interesting class of two-weights metrics with the weight functions depending on the fibre norm of $E$; hence the generalized concept of spherically symmetric metrics. We study its main properties and curvature equations. Finally we focus on a few applications and compute the holonomy of Bryant-Salamon type $mathrm{G}_2$ manifolds.
rate research
Read More
In this paper, we use a Killing form on a Riemannian manifold to construct a class of Finsler metrics. We find equations that characterize Einstein metrics among this class. In particular, we construct a family of Einstein metrics on $S^3$ with ${rm Ric} = 2 F^2$, ${rm Ric}=0$ and ${rm Ric}=- 2 F^2$, respectively. This family of metrics provide an important class of Finsler metrics in dimension three, whose Ricci curvature is a constant, but the flag curvature is not.
We consider canonical fibrations and algebraic geometric structures on homogeneous CR manifolds, in connection with the notion of CR algebra. We give applications to the classifications of left invariant CR structures on semisimple Lie groups and of CR-symmetric structures on complete flag varieties.
A connected Riemannian manifold M has constant vector curvature epsilon, denoted by cvc(epsilon), if every tangent vector v in TM lies in a 2-plane with sectional curvature epsilon. By scaling the metric on M, we can always assume that epsilon = -1, 0, or 1. When the sectional curvatures satisfy the additional bound that each sectional curvature is less than or equal to epsilon, or that each sectional curvature is greater than or equal to epsilon, we say that, epsilon, is an extremal curvature. In this paper we study three-manifolds with constant vector curvature. Our main results show that finite volume cvc(epsilon) three-manifolds with extremal curvature epsilon are locally homogenous when epsilon=-1 and admit a local product decomposition when epsilon=0. As an application, we deduce a hyperbolic rank-rigidity theorem.
In this paper, we classify three-locally-symmetric spaces for a connected, compact and simple Lie group. Furthermore, we give the classification of invariant Einstein metrics on these spaces.
The theory of harmonic vector fields on Riemannian manifolds is generalised to pseudo-Riemannian manifolds. Harmonic conformal gradient fields on pseudo-Euclidean hyperquadrics are classified up to congruence, as are harmonic Killing fields on pseudo-Riemannian quadrics. A para-Kaehler twisted anti-isometry is used to correlate harmonic vector fields on the quadrics of neutral signature.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
