Keywords
- Riemannian Manifold
- Fundamental Form
- Complex Manifold
- Isometric Immersion
- Holonomy Group
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
E. Bonan, "Sur des variétés riemanniennes à groupe d'holonomie G2 ou Spin(7)," C.R. Acad. Sci. Paris 262 (1966), 127–129.
R. Brown and A. Gray, "Vector cross products," Comment. Math. Helv. 42 (1967), 222–236.
E. Calabi, "Construction and properties of some 6-dimensional almost complex manifolds," Trans. Amer. Math. Soc. 87 (1958), 407–438.
G. deRham, "On the area of complex manifolds," Notes, Institute for Advanced Study, Princeton (1957). Part of these notes is contained in a paper of the same title in Global Analysis, papers in honor of K. Kodaira, Princeton, 1969, 141–148.
B. Eckmann, "Systeme von Richtungsfeldern in Sphären und stetige Lösungen komplexer linearer Gleichungen," Comment. Math. Helv. 15 (1943), 1–26.
B. Eckmann, "Continuous solutions of linear equations — some exceptional dimensions in topology," Batelle Rencontres (1967), Lectures in Mathematics and Physics, W.A. Benjamin (1968), 516–526.
J. Eells and L. Lemaire, "A report on harmonic maps," Bull. London Math. Soc. 10 (1978), 1–68.
M. Fernández and A. Gray, "Riemannian manifolds with structure group G2" Ann. Math. Pura Appl. (to appear).
A. Gray, "Vector cross products on manifolds," Trans. Amer. Math. Soc. 141 (1969), 465–504. Correction 148 (1970), 625.
A. Gray, "Riemannian manifolds with geometric symmetries of order 3," J. Differential Geometry 7 (1972), 343–369.
A. Gray, "The structure of nearly Kähler manifolds," Math. Ann. 223 (1976), 233–248.
A. Gray, "Vector cross products," Rend. Sem. Mat. Univ. Politecn. Torino 35 (1976–1977), 69–75.
A. Gray and P. Green, "Sphere transitive structures and the triality automorphism," Pacific J. Math. 34 (1970), 83–96.
A. Gray and L.M. Hervella, "The sixteen classes of almost Hermitian manifolds and their linear invariants," Ann. Mat. Pura Appl. (IV) 123 (1980), 35–58.
R. Harvey and H.B. Lawson, Jr., "A constellation of minimal varieties defined over the group G2," Partial Differential Equations, Proceedings of the Park City Conference (1977), 167–187, Lecture Notes in Pure and Applied Mathematics vol.48, Marcel Dekker, New York, 167–187.
R. Harvey and H.B. Lawson, Jr., "Geometries associated to the group SUn and varieties of minimal submanifolds arising from Cayley arithmetic," preprint IHES, 1978.
S. Marchiafava, "Characterization of Riemannian manifolds with weak holonomy group G2," preprint Università di Roma, 1980.
A. Lichnerowicz, "Sur les applications harmoniques," C.R. Acad. Sci. Paris 267 (1968), A548–553.
A. Lichnerowicz, "Applications harmoniques et variétés kähleriennes," Sym. Math. III, Bologna (1970), 341–402.
G. Whitehead, "Note on cross-sections in Stiefel manifolds," Comment. Math. Helv. 37 (1962), 239–240.
W. Wintinger, "Eine Determinantenidentität unh ihre Anwendung auf analytische Gebilde in Euklidischen und Hermitescher Massbestimmung," Monatsch. f. Math. u. Physik 44 (1936), 343–365.
P. Zvengrowski, "A 3-fold vector product in ℝ8," Comment. Math. Helv. 40 (1966), 149–152.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1982 Springer-Verlag
About this paper
Cite this paper
Gray, A. (1982). Vector cross products, harmonic maps and the Cauchy Riemann equations. In: Knill, R.J., Kalka, M., Sealey, H.C.J. (eds) Harmonic Maps. Lecture Notes in Mathematics, vol 949. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069756
Download citation
DOI: https://doi.org/10.1007/BFb0069756
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11595-3
Online ISBN: 978-3-540-39360-3
eBook Packages: Springer Book Archive
