Conformal Kaehler Euclidean submanifolds

A. de Carvalho; S. Chion; M. Dajczer

doi:10.1016/j.difgeo.2022.101893

Conformal Kaehler Euclidean submanifolds

A. de Carvalho
, S. Chion
, M. Dajczer

IMPA
Universidad de Murcia

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Let f:M²ⁿ→R^2n+ℓ, n≥5, be a conformal immersion into Euclidean space with codimension ℓ where M²ⁿ is a Kaehler manifold of complex dimension n free of points where all sectional curvatures vanish. For codimension ℓ=1 or ℓ=2 we show that at least locally such a submanifold can always be obtained in a rather simple way, namely, from an isometric immersion of the Kaehler manifold M²ⁿ into either R²ⁿ⁺¹ or R²ⁿ⁺², the latter being a class of submanifolds already extensively studied.

Original language	English
Article number	101893
Journal	Differential Geometry and its Application
Volume	82
DOIs	https://doi.org/10.1016/j.difgeo.2022.101893
State	Published - Jun 2022
Externally published	Yes

Keywords

Conformal congruence
Conformal immersion
Real Kaehler submanifold

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10.1016/j.difgeo.2022.101893

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@article{54582d333afa44f3b480beb35ff9d65b,

title = "Conformal Kaehler Euclidean submanifolds",

abstract = "Let f:M2n→R2n+ℓ, n≥5, be a conformal immersion into Euclidean space with codimension ℓ where M2n is a Kaehler manifold of complex dimension n free of points where all sectional curvatures vanish. For codimension ℓ=1 or ℓ=2 we show that at least locally such a submanifold can always be obtained in a rather simple way, namely, from an isometric immersion of the Kaehler manifold M2n into either R2n+1 or R2n+2, the latter being a class of submanifolds already extensively studied.",

keywords = "Conformal congruence, Conformal immersion, Real Kaehler submanifold",

author = "\{de Carvalho\}, A. and S. Chion and M. Dajczer",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",

year = "2022",

month = jun,

doi = "10.1016/j.difgeo.2022.101893",

language = "English",

volume = "82",

journal = "Differential Geometry and its Application",

issn = "0926-2245",

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TY - JOUR

T1 - Conformal Kaehler Euclidean submanifolds

AU - de Carvalho, A.

AU - Chion, S.

AU - Dajczer, M.

PY - 2022/6

Y1 - 2022/6

N2 - Let f:M2n→R2n+ℓ, n≥5, be a conformal immersion into Euclidean space with codimension ℓ where M2n is a Kaehler manifold of complex dimension n free of points where all sectional curvatures vanish. For codimension ℓ=1 or ℓ=2 we show that at least locally such a submanifold can always be obtained in a rather simple way, namely, from an isometric immersion of the Kaehler manifold M2n into either R2n+1 or R2n+2, the latter being a class of submanifolds already extensively studied.

AB - Let f:M2n→R2n+ℓ, n≥5, be a conformal immersion into Euclidean space with codimension ℓ where M2n is a Kaehler manifold of complex dimension n free of points where all sectional curvatures vanish. For codimension ℓ=1 or ℓ=2 we show that at least locally such a submanifold can always be obtained in a rather simple way, namely, from an isometric immersion of the Kaehler manifold M2n into either R2n+1 or R2n+2, the latter being a class of submanifolds already extensively studied.

KW - Conformal congruence

KW - Conformal immersion

KW - Real Kaehler submanifold

UR - https://www.scopus.com/pages/publications/85129467950

U2 - 10.1016/j.difgeo.2022.101893

DO - 10.1016/j.difgeo.2022.101893

M3 - Article

AN - SCOPUS:85129467950

SN - 0926-2245

VL - 82

JO - Differential Geometry and its Application

JF - Differential Geometry and its Application

M1 - 101893

ER -

Conformal Kaehler Euclidean submanifolds

Abstract

Keywords

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