IJPAM: Volume 68, No. 1 (2011)

DIFFERENTIAL GEOMETRY OF
MICROLINEAR FRÖLICHER SPACES III

Hirokazu Nishimura
Institute of Mathematics
University of Tsukuba
Tsukuba, Ibaraki, 305-8571, JAPAN


Abstract. As the third of our series of papers on differential geometry of microlinear Frölicher spaces is this paper devoted to the Frölicher-Nijenhuis calculus of their named bracket. The main result is that the Frölicher-Nijenhuis bracket satisfies the graded Jacobi identity. It is also shown that the Lie derivation preserves the Frölicher-Nijenhuis bracket. Our definitions and discussions are highly geometric, while Frölicher and Nijenhuis' original definitions and discussions were largely algebraic.

Received: January 26, 2011

AMS Subject Classification: 58A40, 58A03, 58A10

Key Words and Phrases: microlinearity, Frölicher space, tangent-vector-valued differential forms, generalized Jacobi identity, graded Lie algebra, Frölicher-Nijenhuis bracket


Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 68
Issue: 1