Rafael Herrera

Centralizers of spin subalgebras

Abstract We determine the centralizers of certain isomorphic copies of spin subalgebras s p i n ( r ) in s o ( d r m ) , where d r is the dimension of a real irreducible representation of C l r 0 , the even Clifford algebra determined by the positive definite inner product on R r , where r , m ∈ N .

Spinorially twisted spin structures, I: Curvature identities and eigenvalue estimates

We define (higher rank) spinorially twisted spin structures and deduce various curvature identites as well as estimates for the eigenvalues of the corresponding twisted Dirac operators.

Almost even-Clifford hermitian manifolds with a large automorphism group

We study manifolds endowed with an (almost) even Clifford (hermitian) structure and admitting a large automorphism group. We classify them when they are simply connected and the dimension of the automorphism group is maximal, and also prove a gap theorem for the dimension of the automorphism group.

A note on the geometry and topology of almost even-Clifford Hermitian manifolds

We compute the structure groups of almost even-Clifford Hermitian manifolds and determine when such groups lead to Spin structures.

Twisted partially pure spinors

Abstract Motivated by the relationship between orthogonal complex structures and pure spinors, we define twisted partially pure spinors in order to characterize spinorially subspaces of Euclidean space endowed with a complex structure.