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