title: Antisymmetric tensor generalizations of affine vector fields.
abstract: Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank-pantisymmetric affine tensor fields inn-dimensions is bounded by (n+ 1)!/p!(n-p)!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes.
authors: Department of Physics, Kobe University , 1-1 Rokkodai, Nada, Kobe, Hyogo 657-8501, Japan.
authors: Tsuyoshi
authors: 0000-0002-3938-1248
authors: T
authors: Houri
authors: Osaka University of Economics and Law , 6-10 Gakuonji, Yao, Osaka 581-8511, Japan.
authors: Yoshiyuki
authors: Y
authors: Morisawa
authors: Department of Physics, Kobe University , 1-1 Rokkodai, Nada, Kobe, Hyogo 657-8501, Japan.
authors: Kentaro
authors: K
authors: Tomoda