Compactness theorems and the Calabi flow on Kähler surfaces with stable tangent bundle

2000 ◽  
Vol 318 (2) ◽  
pp. 315-340 ◽  
Author(s):  
Shu-Cheng Chang
Keyword(s):  
Tangent Bundle ◽  
Calabi Flow ◽  
Kähler Surfaces ◽  
Compactness Theorems

scholarly journals Compactness theorems for critical metrics of the Weyl functional on compact Kähler surfaces

1997 ◽  
Vol 62 (2) ◽  
pp. 217-228
Author(s):  
Shun-Cheng Chang
Keyword(s):  
Einstein Metrics ◽  
Compactness Property ◽  
Critical Metrics ◽  
Kähler Surfaces ◽  
Compactness Theorems ◽  
Kähler Einstein Metrics

AbstractIn this note, we propose an extension of the compactness property for Kähler-Einstein metrics to critical metrics of Weyl functional on compact Kähler surfaces.

The Calabi flow on Kähler Surfaces with bounded Sobolev constant (I)

2011 ◽  
Vol 354 (1) ◽  
pp. 227-261 ◽  
Author(s):  
Xiuxiong Chen ◽  
Weiyong He
Keyword(s):  
Calabi Flow ◽  
Kähler Surfaces ◽  
Sobolev Constant

Golden Riemannian structures on the tangent bundle with g-natural metrics

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2543-2554
Author(s):  
E. Peyghan ◽  
F. Firuzi ◽  
U.C. De
Keyword(s):  
Riemannian Manifold ◽  
Tangent Bundle ◽  
Riemannian Metric

Starting from the g-natural Riemannian metric G on the tangent bundle TM of a Riemannian manifold (M,g), we construct a family of the Golden Riemannian structures ? on the tangent bundle (TM,G). Then we investigate the integrability of such Golden Riemannian structures on the tangent bundle TM and show that there is a direct correlation between the locally decomposable property of (TM,?,G) and the locally flatness of manifold (M,g).

Families over a base with a birationally nef tangent bundle

1997 ◽  
Vol 308 (2) ◽  
pp. 347-359 ◽  
Author(s):  
Sándor J. Kovács
Keyword(s):  
Tangent Bundle

scholarly journals Vortices over Riemann surfaces and dominated splittings

2021 ◽  
pp. 1-26
Author(s):  
THOMAS METTLER ◽  
GABRIEL P. PATERNAIN
Keyword(s):  
Euler Characteristic ◽  
Tangent Bundle ◽  
Riemann Surfaces ◽  
Dominated Splitting ◽  
Vortex Equations ◽  
Special Cases ◽  
Unit Tangent Bundle ◽  
Anosov Flows

Abstract We associate a flow $\phi $ with a solution of the vortex equations on a closed oriented Riemannian 2-manifold $(M,g)$ of negative Euler characteristic and investigate its properties. We show that $\phi $ always admits a dominated splitting and identify special cases in which $\phi $ is Anosov. In particular, starting from holomorphic differentials of fractional degree, we produce novel examples of Anosov flows on suitable roots of the unit tangent bundle of $(M,g)$ .

scholarly journals $$ \mathcal{N} $$ = 2 consistent truncations from wrapped M5-branes

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Davide Cassani ◽  
Grégoire Josse ◽  
Michela Petrini ◽  
Daniel Waldram
Keyword(s):  
Riemann Surface ◽  
Gauge Group ◽  
Tangent Bundle ◽  
Dimensional Manifold ◽  
Five Dimensions ◽  
Intrinsic Torsion ◽  
Consistent Truncations

Abstract We discuss consistent truncations of eleven-dimensional supergravity on a six-dimensional manifold M, preserving minimal $$ \mathcal{N} $$ N = 2 supersymmetry in five dimensions. These are based on GS ⊆ USp(6) structures for the generalised E6(6) tangent bundle on M, such that the intrinsic torsion is a constant GS singlet. We spell out the algorithm defining the full bosonic truncation ansatz and then apply this formalism to consistent truncations that contain warped AdS5×wM solutions arising from M5-branes wrapped on a Riemann surface. The generalised U(1) structure associated with the $$ \mathcal{N} $$ N = 2 solution of Maldacena-Nuñez leads to five-dimensional supergravity with four vector multiplets, one hypermultiplet and SO(3) × U(1) × ℝ gauge group. The generalised structure associated with “BBBW” solutions yields two vector multiplets, one hypermultiplet and an abelian gauging. We argue that these are the most general consistent truncations on such backgrounds.

scholarly journals Minimal Lagrangian surfaces in the tangent bundle of a Riemannian surface

2011 ◽  
Vol 61 (1) ◽  
pp. 237-247 ◽  
Author(s):  
Henri Anciaux ◽  
Brendan Guilfoyle ◽  
Pascal Romon
Keyword(s):  
Tangent Bundle ◽  
Riemannian Surface ◽  
Lagrangian Surfaces ◽  
Minimal Lagrangian Surfaces
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