Quaternionic Transformations of a Non-Positive Quaternionic Kähler Manifold

1997 ◽  
Vol 08 (03) ◽  
pp. 301-316 ◽  
Author(s):  
D. V. Alekseevsky ◽  
S. Marchiafava
Keyword(s):  
Kähler Manifold ◽  
Parameter Group ◽  
Kähler Metric ◽  
Quaternionic Structure ◽  
Kahler Manifold ◽  
Quaternionic Kähler Manifold ◽  
De Rham ◽  
Simply Connected ◽  
Kahler Metric ◽  
Quaternionic Kähler

Let (M,g,Q) be a simply connected, complete, quaternionic Kähler manifold without flat de Rham factor. Then any 1-parameter group of transformations of M which preserve the quaternionic structure Q preserves also the metric g. Moreover, if (M,g) is irreducible then the quaternionic Kähler metric g on (M,Q) is unique up to a homothety.

Conformally Kähler manifolds

1954 ◽  
Vol 50 (1) ◽  
pp. 16-19 ◽  
Author(s):  
W. J. Westlake
Keyword(s):  
Conformal Geometry ◽  
Kähler Manifold ◽  
Hermitian Manifold ◽  
Necessary And Sufficient Condition ◽  
Kähler Metric ◽  
Kahler Manifold ◽  
Hermitian Space ◽  
Necessary And Sufficient ◽  
Simply Connected ◽  
Kahler Metric

Introduction. The present paper is concerned with the conformal geometry of Hermitian spaces. In the first part we find a necessary and sufficient condition for a Hermitian space to be conformally Kähler, that is, conformal to some Kähler space. The condition is that a certain conformal tensor, , vanishes identically. Then, defining a Hermitian manifold as in Hodge (3), we consider such a manifold where the restriction is made that at every point the tensor is zero. This will be called a conformally Kähler manifold, and conditions under which it may be given a Kähler metric are obtained. It is found that any conformally Kähler manifold may be given a Kähler metric provided it is simply-connected or that its fundamental group is of finite order.

scholarly journals TWISTING OF N=1 SUSY GAUGE THEORIES AND HETEROTIC TOPOLOGICAL THEORIES

1995 ◽  
Vol 10 (30) ◽  
pp. 4325-4357 ◽  
Author(s):  
A. JOHANSEN
Keyword(s):  
Complex Structure ◽  
Kähler Manifold ◽  
Dolbeault Cohomology ◽  
Kähler Metric ◽  
Yang Mills ◽  
Kahler Manifold ◽  
Brst Charge ◽  
Kahler Metric ◽  
Compact Kähler Manifold ◽  
Topological Theories

It is shown that D=4N=1 SUSY Yang-Mills theory with an appropriate supermultiplet of matter can be twisted on a compact Kähler manifold. The conditions for cancellation of anomalies of BRST charge are found. The twisted theory has an appropriate BRST charge. We find a nontrivial set of physical operators defined as classes of the cohomology of this BRST operator. We prove that the physical correlators are independent of the external Kähler metric up to a power of a ratio of two Ray-Singer torsions for the Dolbeault cohomology complex on a Kähler manifold. The correlators of local physical operators turn out to be independent of antiholomorphic coordinates defined with a complex structure on the Kähler manifold. However, a dependence of the correlators on holomorphic coordinates can still remain. For a hyper-Kähler metric the physical correlators turn out to be independent of all coordinates of insertions of local physical operators.

THE TIAN–YAU–ZELDITCH ASYMPTOTIC EXPANSION FOR REAL ANALYTIC KÄHLER METRICS

2004 ◽  
Vol 01 (03) ◽  
pp. 253-263 ◽  
Author(s):  
ANDREA LOI
Keyword(s):  
Asymptotic Expansion ◽  
Kähler Manifold ◽  
Distortion Function ◽  
Kähler Metrics ◽  
Kähler Metric ◽  
Kahler Metrics ◽  
Kahler Manifold ◽  
Real Analytic ◽  
Kahler Metric ◽  
Compact Kähler Manifold

Let M be a compact Kähler manifold endowed with a real analytic and polarized Kähler metric g and let Tmω(x) be the corresponding Kempf's distortion function. In this paper we compute the coefficients of Tian–Yau–Zelditch asymptotic expansion of Tmω(x) using quantization techniques alternative to Lu's computations in [10].

scholarly journals Ricci-flat Kähler metrics on canonical bundles

2002 ◽  
Vol 132 (3) ◽  
pp. 471-479 ◽  
Author(s):  
ROGER BIELAWSKI
Keyword(s):  
Kähler Manifold ◽  
Zero Section ◽  
Canonical Bundle ◽  
Kähler Metrics ◽  
Kähler Metric ◽  
Kahler Metrics ◽  
Ricci Flat ◽  
Kahler Manifold ◽  
Real Analytic ◽  
Kahler Metric

We prove the existence of a (unique) S1-invariant Ricci-flat Kähler metric on a neighbourhood of the zero section in the canonical bundle of a real-analytic Kähler manifold X, extending the metric on X.

Quaternionic Kähler Manifold

2004 ◽  
pp. 333-333
Author(s):  
Jian-zu Zhang ◽  
Roberto Floreanini ◽  
Steven Duplij ◽  
Steven Duplij ◽  
Dmitri Gitman ◽  
...  
Keyword(s):  
Kähler Manifold ◽  
Kahler Manifold ◽  
Quaternionic Kähler Manifold ◽  
Quaternionic Kähler

scholarly journals Quaternionic Kähler Metrics Associated to Special Kähler Manifolds with Mutually Local Variations of BPS Structures

2022 ◽  
Author(s):  
Vicente Cortés ◽  
Iván Tulli
Keyword(s):  
Kähler Manifold ◽  
Local Variation ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Kahler Manifold ◽  
Quaternionic Kähler Manifold ◽  
Physics Literature ◽  
Global And Local ◽  
Special Kähler Manifolds ◽  
Quaternionic Kähler

AbstractWe construct a quaternionic Kähler manifold from a conical special Kähler manifold with a certain type of mutually local variation of BPS structures. We give global and local explicit formulas for the quaternionic Kähler metric and specify under which conditions it is positive-definite. Locally, the metric is a deformation of the 1-loop corrected Ferrara–Sabharwal metric obtained via the supergravity c-map. The type of quaternionic Kähler metrics we obtain is related to work in the physics literature by S. Alexandrov and S. Banerjee, where they discuss the hypermultiplet moduli space metric of type IIA string theory, with mutually local D-instanton corrections.

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