Residue: A Geometric Construction

2002 ◽  
Vol 45 (2) ◽  
pp. 284-293 ◽  
Author(s):  
Fernando Sancho de Salas
Keyword(s):  
Geometric Structure ◽  
Differential Forms ◽  
Geometric Construction ◽  
Residue Theorem ◽  
Cohomology Groups ◽  
Local Coordinates ◽  
New Construction

AbstractA new construction of the ordinary residue of differential forms is given. This construction is intrinsic, i.e., it is defined without local coordinates, and it is geometric: it is constructed out of the geometric structure of the local and global cohomology groups of the differentials. The Residue Theorem and the local calculation then follow from geometric reasons.

Vertical Chern Type Classes on Complex Finsler Bundles

2011 ◽  
Vol 57 (2) ◽  
pp. 377-386
Author(s):  
Cristian Ida
Keyword(s):  
Differential Forms ◽  
Linear Connection ◽  
Curvature Form ◽  
Cohomology Groups ◽  
Finsler Manifolds ◽  
Invariance Properties ◽  
Type Classes

Vertical Chern Type Classes on Complex Finsler BundlesIn the present paper, we define vertical Chern type classes on complex Finsler bundles, as an extension of thev-cohomology groups theory on complex Finsler manifolds. These classes are introduced in a classical way by using closed differential forms with respect to the conjugated vertical differential in terms of the vertical curvature form of Chern-Finsler linear connection. Also, some invariance properties of these classes are studied.

VERTICAL TANGENTIAL INVARIANTS ON SOME FOLIATED LAGRANGE SPACES

2013 ◽  
Vol 10 (04) ◽  
pp. 1320002
Author(s):  
CRISTIAN IDA
Keyword(s):  
Tangent Bundle ◽  
Differential Forms ◽  
Characteristic Classes ◽  
Exterior Derivative ◽  
Cohomology Groups ◽  
Foliated Manifold ◽  
Smooth Complex ◽  
De Rham ◽  
Poincaré Lemma ◽  
Natural Decomposition

In this paper we consider a decomposition of tangentially differential forms with respect to the lifted foliation [Formula: see text] to the tangent bundle of a Lagrange space [Formula: see text] endowed with a regular foliation [Formula: see text]. First, starting from a natural decomposition of the tangential exterior derivative along the leaves of [Formula: see text], we define some vertical tangential cohomology groups of the foliated manifold [Formula: see text], we prove a Poincaré lemma for the vertical tangential derivative and we obtain a de Rham theorem for this cohomology. Next, in a classical way, we construct vertical tangential characteristic classes of tangentially smooth complex bundles over the foliated manifold [Formula: see text].

scholarly journals Geometric Construction-Based Realization of Planar Elastic Behaviors With Parallel and Serial Manipulators

2017 ◽  
Vol 9 (5) ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Elastic Properties ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Geometric Construction ◽  
Elastic Component ◽  
Elastic Behavior ◽  
Serial Manipulators ◽  
New Construction ◽  
Necessary And Sufficient ◽  
Serial Mechanism

This paper addresses the passive realization of any selected planar elastic behavior with a parallel or a serial manipulator. Sets of necessary and sufficient conditions for a mechanism to passively realize an elastic behavior are presented. These conditions completely decouple the requirements on component elastic properties from the requirements on mechanism kinematics. The restrictions on the set of elastic behaviors that can be realized with a mechanism are described in terms of acceptable locations of realizable elastic behavior centers. Parallel–serial mechanism pairs that realize identical elastic behaviors (dual elastic mechanisms) are described. New construction-based synthesis procedures for planar elastic behaviors are developed. Using these procedures, one can select the geometry of each elastic component from a restricted space of kinematically allowable candidates. With each selection, the space is further restricted until the desired elastic behavior is achieved.

scholarly journals DEFORMATION THEORY OF THE CHOW GROUP OF ZERO CYCLES

2020 ◽  
Vol 71 (2) ◽  
pp. 677-676
Author(s):  
Morten Lüders
Keyword(s):  
Valuation Ring ◽  
Deformation Theory ◽  
Differential Forms ◽  
Discrete Valuation Ring ◽  
Chow Group ◽  
Cohomology Groups ◽  
Lefschetz Theorems ◽  
Special Fibre

Abstract We study the deformations of the Chow group of zerocycles of the special fibre of a smooth scheme over a Henselian discrete valuation ring. Our main tools are Bloch’s formula and differential forms. As a corollary we get an algebraization theorem for thickened zero cycles previously obtained using idelic techniques. In the course of the proof we develop moving lemmata and Lefschetz theorems for cohomology groups with coefficients in differential forms.

scholarly journals Non-arithmetic lattices and the Klein quartic

2019 ◽  
Vol 2019 (754) ◽  
pp. 253-279 ◽  
Author(s):  
Martin Deraux
Keyword(s):  
Automorphism Group ◽  
Geometric Construction ◽  
Fundamental Groups ◽  
Ball Quotients ◽  
New Construction

Abstract We give an algebro-geometric construction of some of the non-arithmetic ball quotients constructed by the author, Parker and Paupert. The new construction reveals a relationship between the corresponding orbifold fundamental groups and the automorphism group of the Klein quartic, and also with groups constructed by Barthel–Hirzebruch–Höfer and Couwenberg–Heckman–Looijenga.

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