Duality equations on a 4-manifold of conformal torsion-free connection and some of their solutions for the zero signature

Autor: Leonid Nikolaevich Krivonosov, Vyacheslav Anatolievich Lukyanov

Publikováno v: Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, Vol 23, Iss 2, Pp 207-228 (2019)

On a 4-manifold of conformal torsion-free connection with zero signature (--++) we found conditions under which the conformal curvature matrix is dual (self-dual or anti-self-dual). These conditions are 5 partial differential equations of the 2nd ord

Externí odkaz: https://doaj.org/article/a47cf44bd5c84f809773b53ed083ff38

Hermitian metrics with (anti-)self-dual Riemann tensor

Autor: Leonid Nikolaevich Krivonosov, Vyacheslav A Lukyanov

Publikováno v: Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, Vol 25, Iss 4, Pp 616-633 (2021)

Equations of (anti-)self-duality for the components of the Levi-Civita connection of the Hermitian positive definite metric (not for the Riemann tensor) are compiled. With this well-known method, a simpler system of partial differential equations is

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doajarticles::96c0e5200a6001bfb20f3058d2e6a680
http://mi.mathnet.ru/vsgtu1867