scholarly journals Criterion for connections on principal bundles over a pointed Riemann surface

2017 ◽  
Vol 4 (1) ◽  
pp. 155-171 ◽  
Author(s):  
Indranil Biswas
Keyword(s):  
Riemann Surface ◽  
Principal Bundles ◽  
Connections On Principal Bundles

Abstract We investigate connections, and more generally logarithmic connections, on holomorphic principal bundles over a compact connected Riemann surface.

Approximate Hermitian–Einstein connections on principal bundles over a compact Riemann surface

2013 ◽  
Vol 44 (3) ◽  
pp. 257-268 ◽  
Author(s):  
Indranil Biswas ◽  
Steven B. Bradlow ◽  
Adam Jacob ◽  
Matthias Stemmler
Keyword(s):  
Riemann Surface ◽  
Compact Riemann Surface ◽  
Principal Bundles ◽  
Connections On Principal Bundles

scholarly journals A geometric approach to discrete connections on principal bundles

2013 ◽  
Vol 5 (4) ◽  
pp. 433-444 ◽  
Author(s):  
Javier Fernández ◽  
◽  
Marcela Zuccalli ◽  
Keyword(s):  
Geometric Approach ◽  
Principal Bundles ◽  
Connections On Principal Bundles

Connections on Principal Bundles

2015 ◽  
pp. 121-144
Author(s):  
Stephen Bruce Sontz
Keyword(s):  
Principal Bundles ◽  
Connections On Principal Bundles

Variations on the Role of Principal Connections in Robotic Locomotion

2016 ◽  
Author(s):  
Tony Dear ◽  
Scott David Kelly ◽  
Howie Choset
Keyword(s):  
Base Point ◽  
Principal Bundles ◽  
Robotic Locomotion ◽  
Base Manifold ◽  
Terrestrial Locomotion ◽  
Role Of Principal ◽  
Connections On Principal Bundles

Diverse problems in robotic locomotion have previously been modeled in terms of connections on principal bundles. Ordinarily, one identifies points in the base manifold of such a bundle with different internal configurations of a robot, identifies points in the fiber over a given base point with different positions and orientations of the robot in its environment, and assumes control to be applied in the former but not the latter. We examine ways in which the ordinary application of this theory may be adapted to problems in aquatic and terrestrial locomotion that fail to accommodate the preceding description.

scholarly journals On connections on principal bundles

2017 ◽  
Vol 23 (1) ◽  
pp. 32-43
Author(s):  
Indranil Biswas
Keyword(s):  
Principal Bundles ◽  
Connections On Principal Bundles

On holomorphic principal bundles over a compact Riemann surface admitting a flat connection

2002 ◽  
Vol 322 (2) ◽  
pp. 333-346 ◽  
Author(s):  
Hassan Azad ◽  
Indranil Biswas
Keyword(s):  
Riemann Surface ◽  
Compact Riemann Surface ◽  
Flat Connection ◽  
Principal Bundles

scholarly journals Logarithmic connections on principal bundles over a Riemann surface

2017 ◽  
Vol 28 (12) ◽  
pp. 1750088
Author(s):  
Indranil Biswas ◽  
Ananyo Dan ◽  
Arjun Paul ◽  
Arideep Saha
Keyword(s):  
Riemann Surface ◽  
Algebraic Group ◽  
Finite Subset ◽  
Maximal Torus ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Logarithmic Connection ◽  
Connections On Principal Bundles ◽  
Necessary And Sufficient ◽  
Holomorphic Automorphisms

Let [Formula: see text] be a holomorphic principal [Formula: see text]-bundle on a compact connected Riemann surface [Formula: see text], where [Formula: see text] is a connected reductive complex affine algebraic group. Fix a finite subset [Formula: see text], and for each [Formula: see text] fix [Formula: see text]. Let [Formula: see text] be a maximal torus in the group of all holomorphic automorphisms of [Formula: see text]. We give a necessary and sufficient condition for the existence of a [Formula: see text]-invariant logarithmic connection on [Formula: see text] singular over [Formula: see text] such that the residue over each [Formula: see text] is [Formula: see text]. We also give a necessary and sufficient condition for the existence of a logarithmic connection on [Formula: see text] singular over [Formula: see text] such that the residue over each [Formula: see text] is [Formula: see text], under the assumption that each [Formula: see text] is [Formula: see text]-rigid.

GENERAL CONNECTIONS ON PRINCIPAL BUNDLES

2017 ◽  
Vol 20 (4) ◽  
pp. 333-367
Author(s):  
Kensaku Kitada
Keyword(s):  
Principal Bundles ◽  
Connections On Principal Bundles

scholarly journals Flat holomorphic connections on principal bundles over a projective manifold

2004 ◽  
Vol 356 (10) ◽  
pp. 3995-4018 ◽  
Author(s):  
Indranil Biswas ◽  
S. Subramanian
Keyword(s):  
Projective Manifold ◽  
Principal Bundles ◽  
Connections On Principal Bundles
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