Locally symmetric connections on complex surfaces and some equations of Monge-Ampère type

Robaszewska, Maria

doi:10.4310/cag.2008.v16.n2.a5

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Cited by 2 publications

References 7 publications

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On some exact solutions of heavenly equations in four dimensions

Stȩpień

2020

AIP Advances

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Some new classes of exact solutions (so-called functionally invariant solutions) of the elliptic and hyperbolic complex Monge–Ampère equations and of the second heavenly equation are found. Besides, non-invariance of the found classes of solutions of the hyperbolic complex Monge–Ampère equation and the second heavenly equation is investigated—these classes of solutions determine the new classes of metrics without Killing vectors. A criterion of non-invariance of the solutions belonging to the found classes is also formulated.

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On some exact solutions of heavenly equations in four dimensions

Stȩpień

2020

AIP Advances

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On some exact solutions of heavenly equations in four dimensions

Stȩpień¹

2012

Preprint

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Some new classes of exact solutions (so-called functionally invariant solutions) of the elliptic and hyperbolic complex Monge-Ampère equations, the second heavenly equation, mixed heavenly equation, asymmetric heavenly equation and evolution form of second heavenly equation are found. Besides non-invariance of these found classes of solutions has been investigated. These classes of solutions determine the new classes of heavenly metrics without Killing vectors. A criterion of non-invariance of the solutions belonging to found classes, has been also formulated.

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Locally symmetric connections on complex surfaces and some equations of Monge-Ampère type

Abstract: We study locally symmetric connections induced by transversal bundles on non-degenerate complex surfaces. Each of such surfaces together with its transversal bundle can be described locally by a solution to some partial differential equation of Monge-Ampère type.

Cited by 2 publications

References 7 publications

On some exact solutions of heavenly equations in four dimensions

On some exact solutions of heavenly equations in four dimensions

On some exact solutions of heavenly equations in four dimensions

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