For a finite rank projective bundle over a compact manifold, so associated to a torsion, Dixmier-Douady, 3-class, w, on the manifold, we define the ring of differential operators ‘acting on sections of the bundle’ in a formal sense. In particular any oriented even-dimensional manifold carries a projective spin Dirac operator in this sense. More generally the corresponding space of pseudodiffere...

Given a transversely projective foliation F on a C∞ manifold M and a nonnegative integer k, a transversal differential operator DF (2k + 1) of order 2k + 1 from N⊗k to N⊗(−k−1) is constructed, where N denotes the normal bundle for the foliation. There is a natural homomorphism from the space of all infinitesimal deformations of the transversely projective foliation F to the first cohomology of ...

Abstract. In this paper we consider eigenvalues of Schrödinger operator with a weight on compact Riemannian manifolds with boundary (possibly empty) and prove a general inequality for them. By using this inequality, we study eigenvalues of Schrödinger operator with a weight on compact domains in a unit sphere, a complex projective space and a minimal submanifold in a Euclidean space. We also st...

Evaluators and researchers often have to deal with situations in which conventional research tools are impossible to use, either because of the characteristics of a population or unclear research variables. This paper presents a technique that succeeds in overcoming this kind of problem--a projective technique, but one that differs from the usual approach to projective techniques. The approach ...

During recent years, several studies have revealed that human-dog relationships are based on a well-established and complex bond. There is now evidence suggesting that the dog-human affectional bond can be characterized as an "attachment". The present study investigated possible association between the owners' attachment profile assessed throughout a new semi-projective test (the 9 Attachment P...

Abstract In this paper we consider the lower order eigenvalues of biharmonic operator on compact Riemannian manifolds with boundary (possibly empty) and prove a type of general inequalities for them. In particular, we study the lower order eigenvalues of biharmonic operator on compact submanifolds of Euclidean spaces, of spheres, and of projective spaces. We obtain some estimates for lower orde...

Converting a quadrilateral input mesh into a C surface with one bi-3 tensorproduct spline patch per facet is a classical challenge. We give explicit local averaging formulas for the spline control points. Where the quadrilateral mesh is not regular, the patches have two internal double knots, the least number and multiplicity to always allow for an unbiased G construction.

We study the existence of natural and projectively equivariant quantizations for differential operators acting between order 1 vector bundles over a smooth manifold M . To that aim, we make use of the Thomas-Whitehead approach of projective structures and construct a Casimir operator depending on a projective Cartan connection. We attach a scalar parameter to every space of differential operato...

We show that there exists a Lamé operator Ln with projective octahedral monodromy for each n ∈ 1 2 (N + 1 2 ) ∪ 1 3 (N + 1 2 ), and with projective icosahedral monodromy for each n ∈ 1 3 (N+ 1 2 )∪ 1 5 (N+ 1 2 ). To this end, we construct Grothendieck’s dessins d’enfants corresponding to the Belyi morphisms which pull-back hypergeometric operators into Lamé operators Ln with the desired monodro...