Geodesic
Vanishing theorems in affine, Riemannian, and Lorenz geometries
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 1, pp. 35-84

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In this survey, we consider one aspect of the Bochner technique, the proof of vanishing theorems by using the Weitzenbock integral formulas, which allows us to extend the technique to pseudo-Riemannian manifolds and equiaffine connection manifolds. 
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     author = {S. E. Stepanov},
     title = {Vanishing theorems in affine, {Riemannian,} and {Lorenz} geometries},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {35--84},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2005_11_1_a1/}
}
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S. E. Stepanov. Vanishing theorems in affine, Riemannian, and Lorenz geometries. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 1, pp. 35-84. http://geodesic.mathdoc.fr/item/FPM_2005_11_1_a1/