1. While Killing vectors are associated with manifold possessing a Killing tensor. 2. This is technically called a time-like Killing vector . 3. This is a generalization of a Killing vector . 4. However, for various special forms of H, there are additional Killing vector fields. 5. They are a special kind of spinor field related to Killing vector fields and Killing tensors. 6. In the case that \ varphi is identically zero, X is called a Killing vector field. 7. The time translation Killing vector generates a one-parameter group of motion G in the spacetime M. 8. Mathematically, if k ^ a is a suitably normalized Killing vector , then the surface gravity is defined by 9. It commutes with all holomorphic Killing vectors on the cone and in particular with all isometries of the Sasakian manifold. 10. However, in backgrounds with light-like killing vectors , they can considerably simplify the quantization of the string action.
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