# A generalization of the exterior product of differential forms combining Hom-valued forms

Commentationes Mathematicae Universitatis Carolinae (1997)

- Volume: 38, Issue: 3, page 587-602
- ISSN: 0010-2628

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topGross, Christian. "A generalization of the exterior product of differential forms combining Hom-valued forms." Commentationes Mathematicae Universitatis Carolinae 38.3 (1997): 587-602. <http://eudml.org/doc/248094>.

@article{Gross1997,

abstract = {This article deals with vector valued differential forms on $C^\infty $-manifolds. As a generalization of the exterior product, we introduce an operator that combines $\operatorname\{Hom\}(\bigotimes ^s(W),Z)$-valued forms with $\operatorname\{Hom\}(\bigotimes ^s(V),W)$-valued forms. We discuss the main properties of this operator such as (multi)linearity, associativity and its behavior under pullbacks, push-outs, exterior differentiation of forms, etc. Finally we present applications for Lie groups and fiber bundles.},

author = {Gross, Christian},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {differential forms; exterior product; multilinear algebra; differential forms; exterior product; multilinear algebra},

language = {eng},

number = {3},

pages = {587-602},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {A generalization of the exterior product of differential forms combining Hom-valued forms},

url = {http://eudml.org/doc/248094},

volume = {38},

year = {1997},

}

TY - JOUR

AU - Gross, Christian

TI - A generalization of the exterior product of differential forms combining Hom-valued forms

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1997

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 38

IS - 3

SP - 587

EP - 602

AB - This article deals with vector valued differential forms on $C^\infty $-manifolds. As a generalization of the exterior product, we introduce an operator that combines $\operatorname{Hom}(\bigotimes ^s(W),Z)$-valued forms with $\operatorname{Hom}(\bigotimes ^s(V),W)$-valued forms. We discuss the main properties of this operator such as (multi)linearity, associativity and its behavior under pullbacks, push-outs, exterior differentiation of forms, etc. Finally we present applications for Lie groups and fiber bundles.

LA - eng

KW - differential forms; exterior product; multilinear algebra; differential forms; exterior product; multilinear algebra

UR - http://eudml.org/doc/248094

ER -

## References

top- Greub W., Halperin S., Vanstone R., Connections, Curvature, and Cohomology, Vol. II, Academic Press, 1973. Zbl0372.57001
- Gross C., Operators on differential forms for Lie transformation groups, Journal of Lie Theory 6 (1996), 1-17. (1996) Zbl0872.58001MR1406002
- Gross C., Connections on fiber bundles and canonical extensions of differential forms, http://www.mathematik.th-darmstadt.de/prepr, Preprint No. 1795.
- Gross C., Cohomology and connections on fiber bundles and applications to field theories, Journal of Mathematical Physics 37 12 (1996), 6375-6394. (1996) Zbl0863.53017MR1419176
- Helgason S., Differential Geometry and Symmetric Spaces, Academic Press, 1962. Zbl0122.39901MR0145455
- Kobayashi S., Nomizu K., Foundations of Differential Geometry, Vol. I, John Wiley & Sons, 1963. Zbl0526.53001MR1393940

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