scholarly journals A classification of the torsion tensors on almost contact manifolds with B-metric

2014 ◽  
Vol 12 (10) ◽  
Author(s):  
Mancho Manev ◽  
Miroslava Ivanova
Keyword(s):  
Invariant Subspaces ◽  
Structure Group ◽  
Contact Manifolds ◽  
Linear Connections

AbstractThe space of the torsion (0,3)-tensors of the linear connections on almost contact manifolds with B-metric is decomposed in 15 orthogonal and invariant subspaces with respect to the action of the structure group. Three known connections, preserving the structure, are characterized regarding this classification.

Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion–convection equations with weak source

2018 ◽  
Vol 32 (07) ◽  
pp. 1850093
Author(s):  
Ya-Rong Xia ◽  
Shun-Li Zhang ◽  
Xiang-Peng Xin
Keyword(s):  
Nonlinear Diffusion ◽  
Invariant Subspaces ◽  
Complete Classification ◽  
Variable Separation ◽  
Weak Source ◽  
Convection Equation ◽  
Functional Variable ◽  
Diffusion Convection

In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion–convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

CLASSIFICATION OF GAUGE-RELATED INVARIANT CONNECTIONS

1993 ◽  
Vol 05 (01) ◽  
pp. 69-103 ◽  
Author(s):  
R. BAUTISTA ◽  
J. MUCIÑO ◽  
E. NAHMAD-ACHAR ◽  
M. ROSENBAUM
Keyword(s):  
Symmetry Group ◽  
Moduli Space ◽  
Structure Group ◽  
Fiber Bundles ◽  
Explicit Solutions ◽  
Arbitrary Structure ◽  
Holonomy Groups ◽  
Principal Fiber Bundles

Connection 1-forms on principal fiber bundles with arbitrary structure groups are considered, and a characterization of gauge-equivalent connections in terms of their associated holonomy groups is given. These results are then applied to invariant connections in the case where the symmetry group acts transitively on fibers, and both local and global conditions are derived which lead to an algebraic procedure for classifying orbits in the moduli space of these connections. As an application of the developed techniques, explicit solutions for SU (2) × SU (2)-symmetric connections over S2 × S2, with SU(2) structure group, are derived and classified into non-gauge-related families, and multi-instanton solutions are identified.

C*-Algebras Generated by Mappings. Classification of Invariant Subspaces

2018 ◽  
Vol 62 (7) ◽  
pp. 13-30 ◽  
Author(s):  
S. A. Grigoryan ◽  
A. Yu. Kuznetsova
Keyword(s):  
Invariant Subspaces ◽  
C Algebras

REFINEMENT EQUATIONS AND CORRESPONDING LINEAR OPERATORS

2006 ◽  
Vol 04 (03) ◽  
pp. 461-474 ◽  
Author(s):  
VLADIMIR PROTASOV
Keyword(s):  
Invariant Subspaces ◽  
Complete Classification ◽  
Linear Operators ◽  
Refinable Functions ◽  
Computer Design ◽  
Hölder Exponent ◽  
Refinement Equations ◽  
Open Questions ◽  
Compactly Supported Solutions

Refinement equations of the type [Formula: see text] play an exceptional role in the theory of wavelets, subdivision algorithms and computer design. It is known that the regularity of their compactly supported solutions (refinable functions) depends on the spectral properties of special N-dimensional linear operators T0, T1 constructed by the coefficients of the equation. In particular, the structure of kernels and of common invariant subspaces of these operators have been intensively studied in the literature. In this paper, we give a complete classification of the kernels and of all the root subspaces of T0 and T1, as well as of their common invariant subspaces. This result answers several open questions stated in the literature and clarifies the structure of the space spanned by the integer translates of refinable functions. This also leads to some results on the moduli of continuity of refinable functions and wavelets in various functional spaces. In particular, it is proved that the Hölder exponent of those functions is sharp whenever it is not an integer.

A SELF-LINKING FORMULA FOR CURVES IN THE HEISENBERG SPACE

2002 ◽  
Vol 11 (07) ◽  
pp. 1077-1087
Author(s):  
MARCOS M. DINIZ
Keyword(s):  
Dna Structure ◽  
Contact Structures ◽  
Contact Manifolds ◽  
Linking Number ◽  
Legendrian Curves

The formula Lk = Wr + Tw, which expresses the linking number of two curves that bound a ribbon as a sum of two terms, has particularly interested biologists and was used to understand the DNA structure. The study of Legendrian curves in contact manifolds, and in particular in the Heisenberg space, is attached to some important problems in geometry, as the problem of classification of contact structures. In this work, we show the analogue formula for curves in the Heisenberg space, we relate the writhing number with the Thurston-Benequin invariant of a Legendrian curve and derive some results directly from this formula.

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