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.

Type II compact almost homogeneous manifolds of cohomogeneity one-II

2019 ◽  
Vol 30 (13) ◽  
pp. 1940002
Author(s):  
Daniel Guan
Keyword(s):  
Moduli Space ◽  
Kähler Manifold ◽  
Type Ii ◽  
Homogeneous Manifolds ◽  
Kähler Metrics ◽  
Cohomogeneity One ◽  
Kahler Metrics ◽  
Kahler Manifold ◽  
Blowing Up ◽  
Compact Kähler Manifold

In this paper, we start the program of the existence of the smooth equivariant geodesics in the equivariant Mabuchi moduli space of Kähler metrics on type II cohomogeneity one compact Kähler manifold. In this paper, we deal with the manifolds [Formula: see text] obtained by blowing up the diagonal of the product of two copies of a [Formula: see text].

Bergman metrics and geodesics in the space of Kähler metrics on principally polarized abelian varieties

2011 ◽  
Vol 11 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Renjie Feng
Keyword(s):  
Abelian Varieties ◽  
Kähler Manifold ◽  
Invariant Metrics ◽  
Kahler Geometry ◽  
Kähler Metrics ◽  
Complete Asymptotic Expansion ◽  
Kahler Metrics ◽  
Infinite Dimensional ◽  
Kahler Manifold ◽  
Bergman Metrics

AbstractIt is well known in Kähler geometry that the infinite-dimensional symmetric space $\mathcal{H}$ of smooth Kähler metrics in a fixed Kähler class on a polarized Kähler manifold is well approximated by finite-dimensional submanifolds $\mathcal{B}_k\subset\mathcal{H}$ of Bergman metrics of height k. Then it is natural to ask whether geodesics in $\mathcal{H}$ can be approximated by Bergman geodesics in $\mathcal{B}_k$. For any polarized Kähler manifold, the approximation is in the C0 topology. For some special varieties, one expects better convergence: Song and Zelditch proved the C2 convergence for the torus-invariant metrics over toric varieties. In this article, we show that some C∞ approximation exists as well as a complete asymptotic expansion for principally polarized abelian varieties.

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

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.

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