# Structure of the Main Tensor of Conformally Connected Torsion Free Space. Conformal Connections on Hypersurfaces of Projective Space

## Abstract

We give a definition of a conformally connected space with an angular metric of an arbitrary signature. We present basic formulas and classes of such spaces. We obtain the decomposition of the main tensor of a conformally connected torsion free space into irreducible gauge invariant summands and prove that all affine connections obtained from the Levi–Civita connection via the normalization transformation have the same Weyl conformal tensor. We describe all conformal torsion free connections on hypersurfaces of a projective space and give some examples. We construct a global conformal connection on a hyperquadric of the projective space.

- Authors:

- Nizhny Novgorod State Technical University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771210

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 231; Journal Issue: 2; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; CONFORMAL INVARIANCE; DECOMPOSITION; GAUGE INVARIANCE; MATHEMATICAL SPACE; METRICS; TENSORS; WEYL UNIFIED THEORY

### Citation Formats

```
Krivonosov, L. N., E-mail: l.n.krivonosov@gmail.com, and Luk’yanov, V. A., E-mail: oxyzt@ya.ru.
```*Structure of the Main Tensor of Conformally Connected Torsion Free Space. Conformal Connections on Hypersurfaces of Projective Space*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3815-Z.

```
Krivonosov, L. N., E-mail: l.n.krivonosov@gmail.com, & Luk’yanov, V. A., E-mail: oxyzt@ya.ru.
```*Structure of the Main Tensor of Conformally Connected Torsion Free Space. Conformal Connections on Hypersurfaces of Projective Space*. United States. doi:10.1007/S10958-018-3815-Z.

```
Krivonosov, L. N., E-mail: l.n.krivonosov@gmail.com, and Luk’yanov, V. A., E-mail: oxyzt@ya.ru. Tue .
"Structure of the Main Tensor of Conformally Connected Torsion Free Space. Conformal Connections on Hypersurfaces of Projective Space". United States. doi:10.1007/S10958-018-3815-Z.
```

```
@article{osti_22771210,
```

title = {Structure of the Main Tensor of Conformally Connected Torsion Free Space. Conformal Connections on Hypersurfaces of Projective Space},

author = {Krivonosov, L. N., E-mail: l.n.krivonosov@gmail.com and Luk’yanov, V. A., E-mail: oxyzt@ya.ru},

abstractNote = {We give a definition of a conformally connected space with an angular metric of an arbitrary signature. We present basic formulas and classes of such spaces. We obtain the decomposition of the main tensor of a conformally connected torsion free space into irreducible gauge invariant summands and prove that all affine connections obtained from the Levi–Civita connection via the normalization transformation have the same Weyl conformal tensor. We describe all conformal torsion free connections on hypersurfaces of a projective space and give some examples. We construct a global conformal connection on a hyperquadric of the projective space.},

doi = {10.1007/S10958-018-3815-Z},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 2,

volume = 231,

place = {United States},

year = {2018},

month = {5}

}

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