# The super complex Frobenius theorem

C. Denson Hill; Santiago R. Simanca

Annales Polonici Mathematici (1991)

- Volume: 55, Issue: 1, page 139-155
- ISSN: 0066-2216

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topC. Denson Hill, and Santiago R. Simanca. "The super complex Frobenius theorem." Annales Polonici Mathematici 55.1 (1991): 139-155. <http://eudml.org/doc/262243>.

@article{C1991,

abstract = {We formulate and prove a super analogue of the complex Frobenius theorem of Nirenberg.},

author = {C. Denson Hill, Santiago R. Simanca},

journal = {Annales Polonici Mathematici},

keywords = {graded-commutative algebras; supermanifolds; Levi flat super CR structure; locally direct sheaf; super real integrable distribution; super complex Frobenius structure; nilpotent element; derivations; real Frobenius theorem; complex Frobenius theorem},

language = {eng},

number = {1},

pages = {139-155},

title = {The super complex Frobenius theorem},

url = {http://eudml.org/doc/262243},

volume = {55},

year = {1991},

}

TY - JOUR

AU - C. Denson Hill

AU - Santiago R. Simanca

TI - The super complex Frobenius theorem

JO - Annales Polonici Mathematici

PY - 1991

VL - 55

IS - 1

SP - 139

EP - 155

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

LA - eng

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

UR - http://eudml.org/doc/262243

ER -

## References

top- [1] M. Eastwood and C. LeBrun, Thickening and supersymmetric extensions of complex manifolds, Amer. J. Math. 108 (1986), 1177-1192. Zbl0619.53039
- [2] P. Freund, Introduction to Supersymmetry, Cambridge Monographs Math. Phys., Cambridge 1986. Zbl0601.53067
- [3] C. D. Hill and S. R. Simanca, Newlander-Nirenberg theorem on supermanifolds with boundary, preprint, 1990. Zbl0842.32008
- [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. Zbl0662.58008
- [6] D. A. Leites, Introduction to the theory of supermanifolds, Russian Math. Surveys 35 (1980), 3-57. Zbl0439.58007
- [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. Zbl0679.58008
- [9] L. Nirenberg, A Complex Frobenius Theorem, Seminars on Analytic Functions, Vol. 1, Institute of Advanced Study, Princeton 1958. Zbl0099.37502

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