### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 027, 28 pages      arXiv:1609.01509      https://doi.org/10.3842/SIGMA.2017.027

### Rigidity and Vanishing Theorems for Almost Even-Clifford Hermitian Manifolds

Ana Lucia Garcia-Pulido and Rafael Herrera
Centro de Investigación en Matemáticas, A. P. 402, Guanajuato, Gto., C.P. 36000, México

Received October 10, 2016, in final form April 19, 2017; Published online April 23, 2017

Abstract
We prove the rigidity and vanishing of several indices of ''geometrically natural'' twisted Dirac operators on almost even-Clifford Hermitian manifolds admitting circle actions by automorphisms.

Key words: almost even-Clifford Hermitian manifolds; index of elliptic operator; twisted Dirac operators; circle action by automorphisms.

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