Gauge transformations on holomorphic bundles.
Gauge-natural field theories and Noether theorems: canonical covariant conserved currents
Summary: We specialize in a new way the second Noether theorem for gauge-natural field theories by relating it to the Jacobi morphism and show that it plays a fundamental role in the derivation of canonical covariant conserved quantities. In particular we show that Bergmann-Bianchi identities for such theories hold true covariantly and canonically only along solutions of generalized gauge-natural Jacobi equations. Vice versa, all vertical parts of gauge-natural lifts of infinitesimal principal automorphisms...
Gauss curvature estimates for minimal graphs
Gauss-Codazzi tensor fields and the Bonnet immersion theorem.
Gaussian curvature based tangential redistribution of points on evolving surfaces
There exist two main methods for computing a surface evolution, level-set method and Lagrangian method. Redistribution of points is a crucial element in a Lagrangian approach. In this paper we present a point redistribution that compress quads in the areas with a high Gaussian curvature. Numerical method is presented for a mean curvature flow of a surface approximated by quads.
Gaussian weighted unreduced cohomology of locally symmetric spaces.
G-connections as twisted formal solutions of systems of PDE's related to geometric structures
General Affine Differential Geometry for Low Codimension Immersions.
General construction of Banach-Grassmann algebras
We show that a free graded commutative Banach algebra over a (purely odd) Banach space is a Banach-Grassmann algebra in the sense of Jadczyk and Pilch if and only if is infinite-dimensional. Thus, a large amount of new examples of separable Banach-Grassmann algebras arise in addition to the only one example previously known due to A. Rogers.
General Nijenhuis tensor: an example of a secondary invariant
The author considers the Nijenhuis map assigning to two type (1,1) tensor fields , a mapping where , are vector fields. Then is a type (2,1) tensor field (Nijenhuis tensor) if and only if . Considering a smooth manifold with a smooth action of a Lie group, a secondary invariant may be defined as a mapping whose area of invariance is restricted to the inverse image of an invariant subset of under another invariant mapping. The author recognizes a secondary invariant related to the...
General poisson algebras
General Reilly-type inequalities for submanifolds of weighted Euclidean spaces
We prove new upper bounds for the first positive eigenvalue of a family of second order operators, including the Bakry-Émery Laplacian, for submanifolds of weighted Euclidean spaces.
General spectral flow formula for fixed maximal domain
We consider a continuous curve of linear elliptic formally self-adjoint differential operators of first order with smooth coefficients over a compact Riemannian manifold with boundary together with a continuous curve of global elliptic boundary value problems. We express the spectral flow of the resulting continuous family of (unbounded) self-adjoint Fredholm operators in terms of the Maslov index of two related curves of Lagrangian spaces. One curve is given by the varying domains, the other by...
General structured bundles
Summary: [For the entire collection see Zbl 0742.00067.]A general theory of fibre bundles structured by an arbitrary differential-geometric category is presented. It is proved that the structured bundles of finite type coincide with the classical associated bundles.
General theory of Lie derivatives for Lorentz tensors
We show how the ad hoc prescriptions appearing in 2001 for the Lie derivative of Lorentz tensors are a direct consequence of the Kosmann lift defined earlier, in a much more general setting encompassing older results of Y. Kosmann about Lie derivatives of spinors.
General-affine invariants of plane curves and space curves
We present a fundamental theory of curves in the affine plane and the affine space, equipped with the general-affine groups and , respectively. We define general-affine length parameter and curvatures and show how such invariants determine the curve up to general-affine motions. We then study the extremal problem of the general-affine length functional and derive a variational formula. We give several examples of curves and also discuss some relations with equiaffine treatment and projective...
Generalization of Hashiguchi-Ichijyō's theorems to Wagner-type manifolds.
Generalization of p-regularity notion and tangent cone description in the singular case
The theory of p-regularity has approximately twenty-five years’ history and many results have been obtained up to now. The main result of this theory is description of tangent cone to zero set in singular case. However there are numerous nonlinear objects for which the p-regularity condition fails, especially for p > 2. In this paper we generalize the p-regularity notion as a starting point for more detailed consideration based on different p-factor operators constructions.
Generalizations of Melin's inequality to systems
We discuss a recent necessary and sufficient condition for Melin's inequality for a class of systems of pseudodifferential operators.
Generalized Cohomological Index Theories for Lie Group Actions with an Application to Bifurcation Questions for Hamiltonian Systems.