Quaternionic contact hypersurfaces in hyper-Kähler manifolds

J 2017

Quaternionic contact hypersurfaces in hyper-Kähler manifolds

IVANOV, Stefan, Ivan MINCHEV and Dimiter VASSILEV

Basic information

Original name

Quaternionic contact hypersurfaces in hyper-Kähler manifolds

Authors

IVANOV, Stefan (100 Bulgaria), Ivan MINCHEV (100 Bulgaria, guarantor, belonging to the institution) and Dimiter VASSILEV (100 Bulgaria)

Edition

Annali di Matematica Pura ed Applicata, HEIDELBERG, SPRINGER HEIDELBERG, 2017, 0373-3114

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Germany

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 1.066

RIV identification code

RIV/00216224:14310/17:00095899

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1007/s10231-016-0571-x

UT WoS

000393687100012

Keywords in English

Quaternionic contact; Hypersurfaces; Hyper-Kahler; Quaternionic projective space; 3-Sasaki

Abstract

V originále

We describe explicitly all quaternionic contact hypersurfaces (qc-hypersurfaces) in the flat quaternion space Hn+1 and the quaternion projective space. We show that up to a quaternionic affine transformation a qc-hypersurface in Hn+1 is contained in one of the three qc-hyperquadrics in Hn+1. Moreover, we show that an embedded qc-hypersurface in a hyper-Kähler manifold is qc-conformal to a qc-Einstein space and the Riemannian curvature tensor of the ambient hyper-Kähler metric is degenerate along the hypersurface.

Links

3SGA5953, interní kód MU

Name: Kvaternionově kontaktní Yamabeho problém (Acronym: The Quaternionic Contact Yamabe Problem)

Investor: South-Moravian Region, The Quaternionic Contact Yamabe Problem, Incoming grants

Citovat

IVANOV, Stefan, Ivan MINCHEV and Dimiter VASSILEV. Quaternionic contact hypersurfaces in hyper-Kähler manifolds. Annali di Matematica Pura ed Applicata. HEIDELBERG: SPRINGER HEIDELBERG, 2017, vol. 196, No 1, p. 245-267. ISSN 0373-3114. Available from: https://dx.doi.org/10.1007/s10231-016-0571-x.

@article{1358690,
   author = {Ivanov, Stefan and Minchev, Ivan and Vassilev, Dimiter},
   article_location = {HEIDELBERG},
   article_number = {1},
   doi = {http://dx.doi.org/10.1007/s10231-016-0571-x},
   keywords = {Quaternionic contact; Hypersurfaces; Hyper-Kahler; Quaternionic projective space; 3-Sasaki},
   language = {eng},
   issn = {0373-3114},
   journal = {Annali di Matematica Pura ed Applicata},
   title = {Quaternionic contact hypersurfaces in hyper-Kähler manifolds},
   url = {http://link.springer.com/article/10.1007/s10231-016-0571-x/fulltext.html},
   volume = {196},
   year = {2017}
}

TY  - JOUR
ID  - 1358690
AU  - Ivanov, Stefan - Minchev, Ivan - Vassilev, Dimiter
PY  - 2017
TI  - Quaternionic contact hypersurfaces in hyper-Kähler manifolds
JF  - Annali di Matematica Pura ed Applicata
VL  - 196
IS  - 1
SP  - 245-267
EP  - 245-267
PB  - SPRINGER HEIDELBERG
SN  - 03733114
KW  - Quaternionic contact
KW  - Hypersurfaces
KW  - Hyper-Kahler
KW  - Quaternionic projective space
KW  - 3-Sasaki
UR  - http://link.springer.com/article/10.1007/s10231-016-0571-x/fulltext.html
L2  - http://link.springer.com/article/10.1007/s10231-016-0571-x/fulltext.html
N2  - We describe explicitly all quaternionic contact hypersurfaces (qc-hypersurfaces) in the flat quaternion space Hn+1 and the quaternion projective space. We show that up to a quaternionic affine transformation a qc-hypersurface in Hn+1 is contained in one of the three qc-hyperquadrics in Hn+1. Moreover, we show that an embedded qc-hypersurface in a hyper-Kähler manifold is qc-conformal to a qc-Einstein space and the Riemannian curvature tensor of the ambient hyper-Kähler metric is degenerate along the hypersurface.
ER  -

IVANOV, Stefan, Ivan MINCHEV and Dimiter VASSILEV. Quaternionic contact hypersurfaces in hyper-Kähler manifolds. \textit{Annali di Matematica Pura ed Applicata}. HEIDELBERG: SPRINGER HEIDELBERG, 2017, vol.~196, No~1, p.~245-267. ISSN~0373-3114. Available from: https://dx.doi.org/10.1007/s10231-016-0571-x.

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