Finslerian Fields in the Spacetime Tangent Bundle

Finslerian fields are investigated in the arena of the maximal-acceleration invariantspacetime tangent bundle. A variety of differential-geometric Finslerian fields are exposited. Thestructure of Finslerian quantum fields receives particular emphasis. Also, possible generalizedactions are proposed for Finslerian strings and p-branes. 1999 Elsevier Science Ltd.     

Conformal Vector Fields on Finsler Warped Product Manifolds

Acta Mathematica Sinica, English Series - In this paper, we study the conformal vector fields on Finsler warped product manifolds. We obtain a system of equivalent equations that the conformal...     

On the Index of Vector Fields Tangent to Hypersurfaces with Non-Isolated Singularities

Let F be a germ of a holomorphic function at 0 in Cⁿ⁺¹, having0 as a critical point not necessarily isolated, and let be a germ of a holomorphic vectorfield at 0 in Cⁿ⁺¹ with an isolated zero at 0, and tangent toV := F^–1(0). Consider the O_V,0-complex obtained by contractingthe germs of Kähler differential forms of V at 0 (0.1) with the vector field X:=|_Von V: (0.2)     

Tensor Fields of Type (0, 2) on the Tangent Bundle of a Riemannian Manifold

To any (0, 2)-tensor field on the tangent bundle of a Riemannian manifold, we associate a global matrix function. Based on this fact, natural tensor fields are defined and characterized, essentially by means of well-known algebraic results. In the symmetric case, this classification coincides with the one given by Kowalski–Sekizawa; in the skew-symmetric one, it does with that obtained by Janyka.     

Restriction of Tangent Bundle and Semistability

Let G be a simple linear algebraic group defined over ? and P ? G a maximal proper parabolic subgroup such that m: = dim _? G/P ≥ 5. Let ι: Z ₁ ∩ Z ₂?G/P be a smooth complete intersection such that degree(Z _i ) ≥ (m ? 1)·index(G/P)/m, i = 1, 2. Then the vector bundle ι*T(G/P) → Z ₁ ∩ Z ₂ is semistable.     

Some Classes of Almost Anti-Hermitian Structures on the Tangent Bundle

In [11] we have considered a family of natural almost anti-Hermitian structures (G, J) on the tangent bundle TM of a Riemannian manifold (M, g), where the semi-Riemannian metric G is a lift of natural type of g to TM, such that the vertical and horizontal distributions VTM, HTM are maximally isotropic and the almost complex structure J is a usual natural lift of g of diagonal type interchanging VTM, HTM (see [5], [15]). We have obtained the conditions under which this almost anti-Hermitian structure belongs to one of the eight classes of anti-Hermitian manifolds obtained in the classification given in [1]. In this paper we consider another semi-Riemannian metric G on TM such that the vertical and horizontal distributions are orthogonal to each other. We study the conditions under which the above almost complex structure J defines, together with G, an almost anti-Hermitian structure on TM. Next, we obtain the conditions under which this structure belongs to one of the eight classes of anti-Hermitian manifolds obtained in the classification in [1].Partially supported by the Grant 100/2003, MECT-CNCSIS, România.     

Tangent Fields and the Local Structure of Random Fields

A tangent field of a random field X on ^N at a point z is defined to be the limit of a sequence of scaled enlargements of X about z. This paper develops general properties of tangent fields, emphasising their rich structure and strong invariance properties which place considerable constraints on their form. The theory is illustrated by a variety of examples, both of a smooth and fractal nature.     

Conformal Killing Vector Fields and Rellich Type Identities on Riemannian Manifolds, II

We propose a general Noetherian approach to Rellich integral identities. Using this method we obtain a higher order Rellich type identity involving the polyharmonic operator on Riemannian manifolds admitting homothetic transformations. Then we prove a biharmonic Rellich identity in a more general context. We also establish a nonexistence result for semilinear systems involving biharmonic operators.     

Tangent Bundle of a Manifold and its Homotopy Type

There is a homotopy equivalence :MM' between closed smooth manifoldsof an odd dimension such that *TM', TM are stably isomorphicbut not isomorphic to each other.     

On the Tangent Bundle of a Hypersurface in a Riemannian Manifold

Let(Mn, g) and(Nn+1, G) be Riemannian manifolds. Let TMn and TNn+1 be the associated tangent bundles. Let f :(Mn,g) →(Nn+1,G) be an isometrical immersion with g = f*G, F =(f, df) :(TMn, ■) →(TNn+1, Gs) be the isometrical immersion with ■= F*Gs where (df)x: TxM → Tf(x)N for any x ∈M is the differential map, and Gs be the Sasaki metric on TN induced from G. This paper deals with the geometry of TMn as a submanifold of TNn+1 by the moving frame method. The authors firstly study the extrinsic geometry of TMn in TNn+1. Then the integrability of the induced almost complex structure of TM is discussed.     

On the Lagrangian Geometry of the Tangent Bundle of a Toric Variety

Mathematical Notes -     

Kähler Metrics on the Projective Bundle of a Holomorphic Finsler Vector Bundle

Let (M, g) be a compact Kähler manifold and (E, F) be a holomorphic Finsler vector bundle of rank r ≥ 2 over M. In this paper, we prove that there exists a Kähler metric φ defined on the projective bundle P (E) of E, which comes naturally from g and F. Moreover, a necessary and sufficient condition for φ having positive scalar curvature is obtained, and a sufficient condition for φ having positive Ricci curvature is established.     

何时任意常半径的切球丛是Einstein的

研究具有任意常半径r的切球丛,得到该切球丛是Einstein的一个充分必要条件。     

A Vector Bundle of Rank 2 on P1xP3

It is well known that the Horrocks–Mumford bundle F encodesa lot of very interesting geometric information. This is essentiallythe reason for the fact that much work has been done in orderto find other rank-2 bundles on P₄. The only nonsplit vectorbundles of rank 2 on P₄, known up to now, are twists of pullbacksof F by finite coverings f:P₄P₄. So it seems to be a naturalquestion to consider, instead of P₄, other Fano 4-folds. Itis the aim of this note to give an example of a rank-2 vectorbundle on P₁xP₃ and to show that it also admits very interestinggeometric properties.     

The Natural Operators Lifting 1-Forms to r-Jet Prolongation of the Tangent Bundle

We prove that for n-manifolds (n 3) the set of all natural operators T^* T^*(J^rT) is a free [2(r + 1)² + 1]-dimensional module over C (R^r+1). We construct explicitly the basis of the C (R^r+1)-module.     

On the Bergman Theory for Solenoidal and Irrotational Vector Fields. II. Conformal Covariance and Invariance of the Main Objects

This is a continuation of our work (González-Cervantes et al. in On the Bergman theory for solenoidal and irrotational vector fields. I. General theory. Operator theory: advances and applications. Birkhauser, accepted) where for solenoidal and irrotational vector fields theory as well as for the Moisil–Théodoresco quaternionic analysis we introduced the notions of the Bergman space and the Bergman reproducing kernel and studied their main properties. In particular, we described the behavior of the Bergman theory for a given domain whenever the domain is transformed by a conformal map. The formulas obtained hint that the corresponding objects (spaces, operators, etc.) can be characterized as conformally covariant or invariant, and in the present paper we construct a series of categories and functors which allow us to give such characterizations in precise terms.     

Projective Vector Fields on Lorentzian Manifolds

Some relations between the causal character of projective vector fields and curvature on a Lorentzian manifold M are studied. As a consequence, obstructions to the existence of such vector fields are found. Affine, homothetic and Killing vector fields are considered specifically.     

A Global Newton Method for the Nonsmooth Vector Fields on Riemannian Manifolds

Journal of Optimization Theory and Applications - This paper proposes and analyzes a globalized version of the Newton method for finding a singularity of the nonsmooth vector fields. Basically, the...