Compactifications on half-flat manifolds

2005 ◽  
Vol 53 (3) ◽  
pp. 278-336 ◽  
Author(s):  
S. Gurrieri
Keyword(s):  
Flat Manifolds

scholarly journals Crystallographic groups and flat manifolds from surface braid groups

2020 ◽  
pp. 107560
Author(s):  
Daciberg Lima Gonçalves ◽  
John Guaschi ◽  
Oscar Ocampo ◽  
Carolina de Miranda e Pereiro
Keyword(s):  
Braid Groups ◽  
Crystallographic Groups ◽  
Flat Manifolds

scholarly journals Feature detection and tracking in optical flow on non-flat manifolds

2011 ◽  
Vol 32 (15) ◽  
pp. 2047-2052 ◽  
Author(s):  
Sheraz Khan ◽  
Julien Lefevre ◽  
Habib Ammari ◽  
Sylvain Baillet
Keyword(s):  
Optical Flow ◽  
Feature Detection ◽  
Detection And Tracking ◽  
Feature Detection And Tracking ◽  
Flat Manifolds

Second Stiefel-Whitney class and spin structures on flat manifolds of diagonal type

2011 ◽  
Author(s):  
Sergio Console ◽  
Juan Pablo Rossetti ◽  
Roberto J. Miatello ◽  
Carlos Herdeiro ◽  
Roger Picken
Keyword(s):  
Spin Structures ◽  
Whitney Class ◽  
Flat Manifolds

scholarly journals The duality of conformally flat manifolds

2011 ◽  
Vol 42 (1) ◽  
pp. 131-152 ◽  
Author(s):  
Huili Liu ◽  
Masaaki Umehara ◽  
Kotaro Yamada
Keyword(s):  
Conformally Flat ◽  
Conformally Flat Manifolds ◽  
Flat Manifolds

scholarly journals ONE-LOOP EFFECTIVE POTENTIAL FOR SCALAR AND VECTOR FIELDS ON HIGHER-DIMENSIONAL NONCOMMUTATIVE FLAT MANIFOLDS

2001 ◽  
Vol 16 (23) ◽  
pp. 1479-1486 ◽  
Author(s):  
A. A. BYTSENKO ◽  
A. E. GONÇALVES ◽  
S. ZERBINI
Keyword(s):  
Zeta Function ◽  
Vector Fields ◽  
Dimensional Regularization ◽  
Massless Scalar ◽  
Quantum Field Theories ◽  
Dimensional Manifold ◽  
Logarithmic Term ◽  
Scalar And Vector Fields ◽  
The One ◽  
Flat Manifolds

The non-planar contribution to the effective potentials for massless scalar and vector quantum field theories on D-dimensional manifold with p compact noncommutative extra dimensions is evaluated by means of dimensional regularization implemented by zeta function techniques. It is found that, the zeta function associated with the one-loop operator may not be regular at the origin. Thus, the related heat kernel trace has a logarithmic term in the short t asymptotic expansion. Consequences of this fact are briefly discussed.

scholarly journals Solving Liouville-type Problems on Manifolds with Poincaré-Sobolev Inequality by Broadening q-Energy from Finite to Infinite

2017 ◽  
Vol 9 (4) ◽  
pp. 1
Author(s):  
Lina Wu
Keyword(s):  
Riemannian Manifolds ◽  
Sobolev Inequality ◽  
Differential Forms ◽  
Computational Method ◽  
Liouville Type ◽  
Balanced Growth ◽  
Curved Manifolds ◽  
Research Findings ◽  
Liouville Type Results ◽  
Flat Manifolds

The aim of this article is to investigate Liouville-type problems on complete non-compact Riemannian manifolds with Poincaré-Sobolev Inequality. Two significant technical breakthroughs are demonstrated in research findings. The first breakthrough is an extension from non-flat manifolds with non-negative Ricci curvatures to curved manifolds with Ricci curvatures varying among negative values, zero, and positive values. Poincaré-Sobolev Inequality has been applied to overcome difficulties of an extension on manifolds. Poincaré-Sobolev Inequality has offered a special structure on curved manifolds with a mix of Ricci curvature signs. The second breakthrough is a generalization of $q$-energy from finite to infinite. At this point, a technique of $p$-balanced growth has been introduced to overcome difficulties of broadening from finite $q$-energy in $L^q$ spaces to infinite $q$-energy in non-$L^q$ spaces. An innovative computational method and new estimation techniques are illustrated. At the end of this article, Liouville-type results including vanishing properties for differential forms and constancy properties for differential maps have been verified on manifolds with Poincaré-Sobolev Inequality approaching to infinite $q$-energy growth.

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