An estimate for the first eigenvalue of the Dirac operator on compact Riemannian spin manifold admitting parallel one-form Article

Alexandrov, B, Grantcharov, G, Ivanov, S. (1998). An estimate for the first eigenvalue of the Dirac operator on compact Riemannian spin manifold admitting parallel one-form . JOURNAL OF GEOMETRY AND PHYSICS, 28(3-4), 263-270. 10.1016/S0393-0440(97)00080-6

cited authors

  • Alexandrov, B; Grantcharov, G; Ivanov, S

authors

abstract

  • An estimate for the first eigenvalue of the Dirac operator on compact Riemannian spin manifold of positive scalar curvature admitting a parallel one-form is found. The possible universal covering spaces of the manifolds on which the smallest possible eigenvalue is attained are also listed. Moreover, a complete classification of the compact odd-dimensional manifolds whose universal covering space is Sn-1 × ℝ is given in the limiting case. All such manifolds are diffeomorphic but not necessarily isometric to Sn-1 × S1. © 1998 Elsevier Science B.V.

publication date

  • January 1, 1998

published in

Digital Object Identifier (DOI)

start page

  • 263

end page

  • 270

volume

  • 28

issue

  • 3-4