The Lichnerowicz-Weitzenböck formula and superconductivity

2013 ◽  
Vol 54 (1) ◽  
pp. 013101 ◽  
Author(s):  
Alfredo A. Vargas-Paredes ◽  
Mauro M. Doria ◽  
José Abdala Helayël Neto
Keyword(s):  
Weitzenböck Formula

HORIZONTAL LAPLACIAN ON TANGENT BUNDLE OF FINSLER MANIFOLD WITH g-NATURAL METRIC

2012 ◽  
Vol 09 (07) ◽  
pp. 1250061 ◽  
Author(s):  
ESMAEIL PEYGHAN ◽  
AKBAR TAYEBI ◽  
CHUNPING ZHONG
Keyword(s):  
Tangent Bundle ◽  
Vector Fields ◽  
Vector Bundles ◽  
Killing Vector ◽  
Finsler Manifold ◽  
Order Differential Operator ◽  
Finsler Manifolds ◽  
Scalar And Vector Fields ◽  
Matsumoto Metric ◽  
Weitzenböck Formula

Recently the third author studied horizontal Laplacians in real Finsler vector bundles and complex Finsler manifolds. In this paper, we introduce a class of g-natural metrics Ga,b on the tangent bundle of a Finsler manifold (M, F) which generalizes the associated Sasaki–Matsumoto metric and Miron metric. We obtain the Weitzenböck formula of the horizontal Laplacian associated to Ga,b, which is a second-order differential operator for general forms on tangent bundle. Using the horizontal Laplacian associated to Ga,b, we give some characterizations of certain objects which are geometric interest (e.g. scalar and vector fields which are horizontal covariant constant) on the tangent bundle. Furthermore, Killing vector fields associated to Ga,b are investigated.

SOME RESULTS ON HARMONIC MAPS FOR FINSLER MANIFOLDS

2005 ◽  
Vol 16 (09) ◽  
pp. 1017-1031 ◽  
Author(s):  
QUN HE ◽  
YI-BING SHEN
Keyword(s):  
Riemannian Manifold ◽  
Harmonic Maps ◽  
Harmonic Map ◽  
Energy Functional ◽  
Second Variation ◽  
Finsler Manifolds ◽  
Totally Geodesic ◽  
The Stability ◽  
The Second Variation ◽  
Weitzenböck Formula

By simplifying the first and the second variation formulas of the energy functional and generalizing the Weitzenböck formula, we study the stability and the rigidity of harmonic maps between Finsler manifolds. It is proved that any nondegenerate harmonic map from a compact Einstein Riemannian manifold with nonnegative scalar curvature to a Berwald manifold with nonpositive flag curvature is totally geodesic and there is no nondegenerate stable harmonic map from a Riemannian unit sphere Sn (n > 2) to any Finsler manifold.

scholarly journals Bochner–Weitzenböck formula and Li–Yau estimates on Finsler manifolds

2014 ◽  
Vol 252 ◽  
pp. 429-448 ◽  
Author(s):  
Shin-ichi Ohta ◽  
Karl-Theodor Sturm
Keyword(s):  
Finsler Manifolds ◽  
Weitzenböck Formula

scholarly journals Weitzenböck Formula for SL(q)-foliations

2010 ◽  
Vol 58 (2) ◽  
pp. 179-188 ◽  
Author(s):  
Adam Bartoszek ◽  
Jerzy Kalina ◽  
Antoni Pierzchalski
Keyword(s):  
Weitzenböck Formula

scholarly journals The WeitzenbÕck formula for the Bach operator

1995 ◽  
Vol 137 ◽  
pp. 149-181 ◽  
Author(s):  
Mitsuhiro Itoh
Keyword(s):  
Riemannian Metrics ◽  
The Self ◽  
Weitzenböck Formula ◽  
Hodge Star Operator

(Anti-)self-dual metrics are 4-dimensional Riemannian metrics whose Weyl conformai tensor W half vanishes. The Weyl conformai tensor W of an arbitrary metric on an oriented 4-manifold has in general the self-dual part W+ and the anti-self-dual part W− with respect to the Hodge star operator * and one says that a metric is self-dual or anti-self-dual if W− = 0 or W+ = 0, respectively.

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