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The Dolbeault operator on Hermitian spin surfaces

Bodgan Alexandrov, Gueo Grantcharov, Stefan Ivanov (2001)

Annales de l’institut Fourier

We prove the vanishing of the kernel of the Dolbeault operator of the square root of the canonical line bundle of a compact Hermitian spin surface with positive scalar curvature. We give lower estimates of the eigenvalues of this operator when the conformal scalar curvature is non -negative.

Vanishing conharmonic tensor of normal locally conformal almost cosymplectic manifold

Farah H. Al-Hussaini, Aligadzhi R. Rustanov, Habeeb M. Abood (2020)

Commentationes Mathematicae Universitatis Carolinae

The main purpose of the present paper is to study the geometric properties of the conharmonic curvature tensor of normal locally conformal almost cosymplectic manifolds (normal LCAC-manifold). In particular, three conhoronic invariants are distinguished with regard to the vanishing conharmonic tensor. Subsequentaly, three classes of normal LCAC-manifolds are established. Moreover, it is proved that the manifolds of these classes are η -Einstein manifolds of type ( α , β ) . Furthermore, we have determined...

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