On 2-dimensional surfaces in 3-dimensional and 4-dimensional Euclidean spaces. Results and unsolved problems

• Datum: 2019
• Hauptverfasser: Aminov, Yu. A., Аминов, Ю. А.
• Format: Artikel
• Sprache: Russisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2019
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/1416
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We present a survey of the results obtained for 2-dimensional surfaces in $E^3$ and $E^4$ and connected with the Gaussian curvature and Gaussian torsion. In this connection, we consider the Monge –Amp´ere equations, obtain the generalizations of Bernstein’s integral formula, and establish some lower...