Determinants of Laplacians in real line bundles over hyperbolic manifolds connected with quantum geometry of membranes

1990 ◽  
Vol 19 (1) ◽  
pp. 73-81 ◽  
Author(s):  
Yu. P. Goncharov
Keyword(s):  
Real Line ◽  
Hyperbolic Manifolds ◽  
Line Bundles ◽  
Quantum Geometry ◽  
Determinants Of Laplacians

EVALUATION OF A CLASS OF THE LAPLACE OPERATOR DETERMINANTS CONNECTED WITH QUANTUM GEOMETRY OF p-BRANES

1991 ◽  
Vol 06 (08) ◽  
pp. 669-675 ◽  
Author(s):  
A.A. BYTSENKO ◽  
YU. P. GONCHAROV
Keyword(s):  
Laplace Operator ◽  
Trace Formula ◽  
Real Line ◽  
Line Bundles ◽  
Riemannian Surface ◽  
Quantum Geometry ◽  
Selberg Trace Formula ◽  
Riemannian Surfaces ◽  
Determinants Of Laplacians ◽  
The Laplace Operator

We evaluate the determinants of Laplacians acting in real line bundles over the manifolds Tp−1×H2/Γ, T=S1, H2/Γ is a compact Riemannian surface of genus g>1. Such determinants may be important in building quantum geometry of closed p-branes. The evaluation is based on the Selberg trace formula for compact Riemannian surfaces.

scholarly journals DETERMINANT LINE BUNDLES AND TOPOLOGICAL INVARIANTS OF HYPERBOLIC GEOMETRY

2002 ◽  
Vol 17 (06n07) ◽  
pp. 951-955
Author(s):  
ANDREI A. BYTSENKO
Keyword(s):  
Dirac Operator ◽  
Hyperbolic Geometry ◽  
Hyperbolic Manifolds ◽  
Line Bundles ◽  
Topological Invariants ◽  
Twisted Dirac Operator ◽  
Determinant Line Bundles

Some remarks on determinant line bundles and topological invariants are given. The index of the twisted Dirac operator acting on real hyperbolic manifolds is computed. We briefly discuss physical applications of results.

scholarly journals Real line bundles on spheres

1971 ◽  
Vol 27 (3) ◽  
pp. 579-579 ◽  
Author(s):  
Allan L. Edelson
Keyword(s):  
Real Line ◽  
Line Bundles

Approximation in statistical sense to B -continuous functions by positive linear operators

2010 ◽  
Vol 47 (3) ◽  
pp. 289-298 ◽  
Author(s):  
Fadime Dirik ◽  
Oktay Duman ◽  
Kamil Demirci
Keyword(s):  
Compact Subset ◽  
Real Line ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Classical Version ◽  
Statistical Sense

In the present work, using the concept of A -statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B -continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.

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