On warped product manifolds satisfying some curvature conditions

We determine curvature properties of pseudosymmetric type of certain warped product manifolds, and in particular of generalized Robertson–Walker spacetimes, with Einsteinian or quasi-Einsteinian fibre.     

On nondegenerate coupling forms

The aim of the present paper is to investigate new classes of symplectically fat fibre bundles. We prove a general existence theorem for fat vectors with respect to the canonical invariant connections. Based on this result we give new proofs of some constructions of symplectic structures. This includes twistor bundles and locally homogeneous complex manifolds. The proofs are conceptually simpler and allow for obtaining more general results.     

Cotilting modules with finite left perpendicular categories

We characterize a cotilting module T such that the left perpendicular category ⊥ T is of finite type.     

Intrinsic ultracontractivity on Riemannian manifolds with infinite volume measures

By establishing the intrinsic super-Poincar'e inequality,some explicit conditions are presented for diffusion semigroups on a non-compact complete Riemannian manifold to be intrinsically ultracontractive.These conditions,as well as the resulting uniform upper bounds on the intrinsic heat kernels,are sharp for some concrete examples.     

Multiplication Modules and a Theorem of P. F. Smith

P. F. Smith [7, Theorem 8] gave sufficient conditions on a finite set of modules for their sum and intersection to be multiplication modules. We give sufficient conditions on an arbitrary set of multiplication modules for the intersection to be a multiplication module. We generalize Smith"s theorem, and we prove conditions on sums and intersections of sets of modules sufficient for them to be multiplication modules. This revised version was published online in June 2006 with corrections to the Cover Date.     

ON NONLINEAR DIFFERENTIAL GALOIS THEORY

This Is an accom ofa work In course ofprogress．The aim Is the following:     

Cyclic Group Actions on 4-Manifolds

Let X be a closed, oriented Riemannian 4-manifold. Suppose that a cyclic group Z( _p (p is prime) acts on X by an orientation preserving isometry with an embedded Riemann surface as fixed point set. We study the representation of Z _p on the Spin^c-bundles and the Z _p-invariant moduli space of the solutions of the Seiberg–Witten equations for a Spin^c-structure X. When the Z _p action on the determinant bundle det L acts non-trivially on the restriction L| over the fixed point set , we consider -twisted solutions of the Seiberg-Witten equations over a Spin^c-structure ' on the quotient manifold X/Z _p X', (0,1). We relate the Z _p -invariant moduli space for the Spin^c-structure on X and the -twisted moduli space for the Spin^c-structure on X'. From this we induce a one-to-one correspondence between these moduli spaces and calculate the dimension of the -twisted moduli space. When Z _p acts trivially on L|, we prove that there is a one-to-one correspondence between the Z _p -invariant moduli space M( ^Zp and the moduli space M (") where ' is a Spin^c-structure on X' associated to the quotient bundle L/Z _p X'. vskip0pt When p = 2, we apply the above constructions to a Kahler surface X with b ₂ ⁺ (X) > 3 and H ₂(X;Z) has no 2-torsion on which an anti-holomorphic involution acts with fixed point set , a Lagrangian surface with genus greater than 0 and []2H ₂(H ;Z). If _K ^X 2 > 0 or K _X ² = 0 and the genus g()> 1, we have a vanishing theorem for Seiberg–Witten invariant of the quotient manifold X'. When K _X ² = 0 and the genus g()= 1, if there is a Z ²-equivariant Spin^c-structure on X whose virtual dimension of the Seiberg–Witten moduli space is zero then there is a Spin^c-structure " on X' such that the Seiberg-Witten invariant is ±1.     

On multiplicities of simple subquotients in generalized Verma modules

We reduce the problem on multiplicities of simple subquotients in an -stratified generalized Verma module to the analogous problem for classical Verma modules.     

Newton's method on Riemannian manifolds and a geometric model for the human spine

To study a geometric model of the human spine we are led tofinding a constrained minimum of a real valued function definedon a product of special orthogonal groups. To take advantgeof its Lie group structure we consider Newton's method on thismanifold. Comparisons between measured spines and computed spinesshow the pertinence of this approach.