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Tritangent planes to toroidal knots.

A. Montesinos Amilibia (1991)

Revista Matemática de la Universidad Complutense de Madrid

A proof is given that, with the only exception of (3,2), all toroidal knots in R3 obtained in the standard way by stereographic projection of knots in S3 have tritangent planes.

TT-tensors and conformally flat structures on 3-manifolds

R. Beig (1997)

Banach Center Publications

We study TT-tensors on conformally flat 3-manifolds (M,g). The Cotton-York tensor linearized at g maps every symmetric tracefree tensor into one which is TT. The question as to whether this is the general solution to the TT-condition is viewed as a cohomological problem within an elliptic complex first found by Gasqui and Goldschmidt and reviewed in the present paper. The question is answered affirmatively when M is simply connected and has vanishing 2nd de Rham cohomology.

Twisted spherical means in annular regions in n and support theorems

Rama Rawat, R.K. Srivastava (2009)

Annales de l’institut Fourier

Let Z ( Ann ( r , R ) ) be the class of all continuous functions f on the annulus Ann ( r , R ) in n with twisted spherical mean f × μ s ( z ) = 0 , whenever z n and s > 0 satisfy the condition that the sphere S s ( z ) Ann ( r , R ) and ball B r ( 0 ) B s ( z ) . In this paper, we give a characterization for functions in Z ( Ann ( r , R ) ) in terms of their spherical harmonic coefficients. We also prove support theorems for the twisted spherical means in n which improve some of the earlier results.

Twistor forms on Kähler manifolds

Andrei Moroianu, Uwe Semmelmann (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Twistor forms are a natural generalization of conformal vector fields on riemannian manifolds. They are defined as sections in the kernel of a conformally invariant first order differential operator. We study twistor forms on compact Kähler manifolds and give a complete description up to special forms in the middle dimension. In particular, we show that they are closely related to hamiltonian 2-forms. This provides the first examples of compact Kähler manifolds with non–parallel twistor forms in...

Twistor operators on conformally flat spaces

Somberg, Petr (2001)

Proceedings of the 20th Winter School "Geometry and Physics"

Summary: We describe explicitly the kernels of higher spin twistor operators on standard even dimensional Euclidean space 2 l , standard even dimensional sphere S 2 l , and standard even dimensional hyperbolic space 2 l , using realizations of invariant differential operators inside spinor valued differential forms. The kernels are finite dimensional vector spaces (of the same cardinality) generated by spinor valued polynomials on 2 l , S 2 l , 2 l .

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