Structural equations of supermanifolds immersed in the superspace M-(3 vertical bar 2) (c) with a prescribed curvature

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F18%3A00328295" target="_blank" >RIV/68407700:21340/18:00328295 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1088/1751-8121/aac971" target="_blank" >http://dx.doi.org/10.1088/1751-8121/aac971</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1751-8121/aac971" target="_blank" >10.1088/1751-8121/aac971</a>

Result language

angličtina

Original language name

Structural equations of supermanifolds immersed in the superspace M-(3 vertical bar 2) (c) with a prescribed curvature

Original language description

The aim of this paper is to construct the structural equations of supermanifolds immersed in Euclidean, hyperbolic and spherical superspaces parametrised with two bosonic and two fermionic variables. To perform this analysis, for each type of immersion, we split the supermanifold into its Grassmannian components and study separately each manifold generated. Even though we consider four variables in the Euclidean case, we obtain that the structural equations of each manifold are linked with the Gauss-Codazzi equations of a surface immersed in a Euclidean or spherical space. In the hyperbolic and spherical superspaces, we find that the body manifolds are linked with the classical Gauss-Codazzi equations for a surface immersed in hyperbolic and spherical spaces, respectively. For some soul manifolds, we show that the immersion of the manifolds must be in a hyperbolic space and that the structural equations split into two cases. In one case, the structural equations reduce to the Liouville equation, which can be completely solved. In the other case, we can express the geometric quantities solely in terms of the metric coefficients, which provide a geometric characterization of the structural equations in terms of functions linked with the Hopf differential, the mean curvature and a new function which does not appear in the characterization of a classical (not super) surface.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10100 - Mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Physics A: Mathematical and Theoretical

ISSN

1751-8113

e-ISSN

1751-8121

Volume of the periodical

51

Issue of the periodical within the volume

30

Country of publishing house

GB - UNITED KINGDOM

Number of pages

20

Pages from-to

—

UT code for WoS article

000435721700002

EID of the result in the Scopus database

—