| Sumario: | In the present work, a family of Calabi-Yau manifolds with a local Hamiltonian Killing vector is described in terms of a nonlinear equation whose solutions determine the local form of the geometries. The main assumptions are that the complex (3, 0)-form is of the form eikΨ̄, where Ψ̄ is preserved by the Killing vector, and that the space of the orbits of the Killing vector is, for fixed value of the momentum map coordinate, a complex 4-manifold, in such a way that the complex structure of the 4-manifold is part of the complex structure of the complex 3-fold. The family considered here include the ones considered in A. Fayyazuddin, Classical Quantum GravityCQGRDG0264-9381 24, 3151 (2007)10.1088/0264-9381/24/13/002; O.P. Santillan, Classical Quantum GravityCQGRDG0264-9381 27, 155013 (2010)10.1088/0264-9381/27/15/155013; H. Lu, Y. Pang, and Z. Wang, Classical Quantum GravityCQGRDG0264-9381 27, 155018 (2010)10.1088/0264-9381/27/15/155018 as a particular case. We also present an explicit example with holonomy exactly SU(3) by use of the linearization introduced in A. Fayyazuddin, Classical Quantum GravityCQGRDG0264-9381 24, 3151 (2007)10.1088/0264-9381/24/13/002, which was considered in the context of D6 branes wrapping a complex 1-cycle in a hyperkahler 2-fold. © 2010 The American Physical Society.
|
|---|