A finiteness theorem for quaternionic-Kähler manifolds with positive scalar curvature

1993 ◽  
pp. 89-101 ◽  
Author(s):  
Claude LeBrun
Keyword(s):  
Scalar Curvature ◽  
Positive Scalar Curvature ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Finiteness Theorem ◽  
Positive Scalar ◽  
Quaternionic Kähler

scholarly journals PARTIAL CLASSIFICATION RESULTS FOR POSITIVE QUATERNION KÄHLER MANIFOLDS

2012 ◽  
Vol 23 (02) ◽  
pp. 1250038
Author(s):  
MANUEL AMANN
Keyword(s):  
Scalar Curvature ◽  
Riemannian Manifolds ◽  
Symmetric Spaces ◽  
Positive Scalar Curvature ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
The Real ◽  
Positive Scalar ◽  
Partial Classification ◽  
Almost All

Positive Quaternion Kähler Manifolds are Riemannian manifolds with holonomy contained in Sp(n)Sp(1) and with positive scalar curvature. Conjecturally, they are symmetric spaces. We prove this conjecture in dimension 20 under additional assumptions and we provide recognition theorems for the real Grassmannian [Formula: see text] in almost all dimensions.

FANO MANIFOLDS WITH GEOMETRIC STRUCTURES MODELED AFTER HOMOGENEOUS CONTACT MANIFOLDS

2000 ◽  
Vol 11 (09) ◽  
pp. 1203-1230 ◽  
Author(s):  
JAEHYUN HONG
Keyword(s):  
Symmetric Space ◽  
Scalar Curvature ◽  
Positive Scalar Curvature ◽  
Geometric Structures ◽  
Contact Manifolds ◽  
Fano Manifolds ◽  
Positive Scalar ◽  
Model Spaces ◽  
Quaternionic Kähler Manifold ◽  
Quaternionic Kähler

In this paper we present a study on geometric structures modeled after homogeneous contact manifolds and show that on Fano manifolds these geometric structures are locally isomorphic to the standard geometric structures on the model spaces. This conclusion is analogous to those of [13, 7]. We expect that this work will help prove the conjecture that a compact quaternionic Kähler manifold of positive scalar curvature is a quaternionic symmetric space [21].

The Twistor Space of a 3-Sasakian Manifold

1997 ◽  
Vol 08 (01) ◽  
pp. 31-60 ◽  
Author(s):  
Charles P. Boyer ◽  
Krzysztof Galicki
Keyword(s):  
Scalar Curvature ◽  
Smooth Manifold ◽  
Twistor Space ◽  
Sasakian Manifold ◽  
Positive Scalar Curvature ◽  
Einstein Metric ◽  
Singular Case ◽  
Positive Scalar ◽  
Smooth Case ◽  
Quaternionic Kähler

Any compact 3-Sasakian manifold [Formula: see text] is a principal circle V-bundle over a compact complex orbifold [Formula: see text]. This orbifold has a contact Fano structure with a Kähler–Einstein metric of positive scalar curvature and it is the twistor space of a positive compact quaternionic Kähler orbifold [Formula: see text]. We show that many results known to hold when [Formula: see text] is a smooth manifold extend to this more general singular case. However, we construct infinite families of examples with [Formula: see text] which sharply differs from the smooth case, where there is only one such [Formula: see text].

Positive scalar curvature metrics via end-periodic manifolds

2020 ◽  
Vol 5 (3) ◽  
pp. 639-676
Author(s):  
Michael Hallam ◽  
Varghese Mathai
Keyword(s):  
Scalar Curvature ◽  
Positive Scalar Curvature ◽  
Positive Scalar

scholarly journals Curvature of quaternionic Kähler manifolds with $$S^1$$-symmetry

2021 ◽  
Author(s):  
V. Cortés ◽  
A. Saha ◽  
D. Thung
Keyword(s):  
Curvature Tensor ◽  
Decomposition Theorem ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Riemann Curvature ◽  
Riemann Curvature Tensor ◽  
Cohomogeneity One ◽  
Civita Connection ◽  
Levi Civita Connection ◽  
Quaternionic Kähler

AbstractWe study the behavior of connections and curvature under the HK/QK correspondence, proving simple formulae expressing the Levi-Civita connection and Riemann curvature tensor on the quaternionic Kähler side in terms of the initial hyper-Kähler data. Our curvature formula refines a well-known decomposition theorem due to Alekseevsky. As an application, we compute the norm of the curvature tensor for a series of complete quaternionic Kähler manifolds arising from flat hyper-Kähler manifolds. We use this to deduce that these manifolds are of cohomogeneity one.

scholarly journals Complete hypersurfaces in cylinders

1989 ◽  
Vol 46 (2) ◽  
pp. 313-318
Author(s):  
Thomas Hasanis
Keyword(s):  
Euclidean Space ◽  
Scalar Curvature ◽  
Sectional Curvature ◽  
Positive Scalar Curvature ◽  
Positive Scalar ◽  
Coordinate Functions ◽  
Bounded Below ◽  
Complete Hypersurfaces

AbstractWe consider the extent of certain complete hypersurfaces of Euclidean space. We prove that every complete hypersurface in En+1 with sectional curvature bounded below and non-positive scalar curvature has at least (n − 1) unbounded coordinate functions.

Sign in / Sign up

Export Citation Format

Share Document