The super complex Frobenius theorem

• Autorzy: C. Denson Hill , Santiago R. Simanca
• Języki publikacji: EN

Abstrakty

EN

We formulate and prove a super analogue of the complex Frobenius theorem of Nirenberg.

Słowa kluczowe

EN

graded-commutative algebras; supermanifolds; Levi flat super CR structure; locally direct sheaf; super real integrable distribution; super complex Frobenius structure; nilpotent element; derivations

Kategorie tematyczne

• 58A50: Supermanifolds and graded manifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1991
• Tom: 55
• Numer: 1
• Strony: 139-155

Daty

wydano

1991

otrzymano

1990-09-12

Twórcy

autor

C. Denson Hill

• Department of Mathematics, State University of New York, Stony Brook, New York 11794, U.S.A.

autor

Santiago R. Simanca

• Department of Mathematics, State University of New York, Stony Brook, New York 11794, U.S.A.

Bibliografia

• [1] M. Eastwood and C. LeBrun, Thickening and supersymmetric extensions of complex manifolds, Amer. J. Math. 108 (1986), 1177-1192.
• [2] P. Freund, Introduction to Supersymmetry, Cambridge Monographs Math. Phys., Cambridge 1986.
• [3] C. D. Hill and S. R. Simanca, Newlander-Nirenberg theorem on supermanifolds with boundary, preprint, 1990.
• [4] B. Kostant, Graded manifolds, graded Lie algebras, and prequantization, in: Lecture Notes in Math. 570, Springer, 1977, 177-306.
• [5] C. LeBrun and M. Rothstein, Moduli of super Riemann surfaces, Comm. Math. Phys. 117 (1988), 159-176.
• [6] D. A. Leites, Introduction to the theory of supermanifolds, Russian Math. Surveys 35 (1980), 3-57.
• [7] Yu. I. Manin, Gauge Field Theory and Complex Geometry, Grundlehren Math. Wiss. 289, Springer, 1988 (Russian original published by Nauka, Moscow 1984).
• [8] A. McHugh, A Newlander-Nirenberg theorem for super-manifolds, J. Math. Phys. 30 (5) (1989), 1039-1042.
• [9] L. Nirenberg, A Complex Frobenius Theorem, Seminars on Analytic Functions, Vol. 1, Institute of Advanced Study, Princeton 1958.