Complete cscK Metrics on the Local Models of the Conifold Transition

Jixiang Fu; Shing Tung Yau; Wubin Zhou

doi:10.1007/s00220-015-2337-5

Complete cscK Metrics on the Local Models of the Conifold Transition

Jixiang Fu^*
, Shing Tung Yau
, Wubin Zhou

^*Corresponding author for this work

Fudan University
Harvard University
Shanghai Center for Mathematical Sciences

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

5 Citations (Scopus)

Abstract

In this paper, we construct complete constant scalar curvature Kähler (cscK) metrics on the complement of the zero section in the total space of (Formula Presented) over P¹, which is biholomorphic to the smooth part of the cone C₀ in C⁴ defined by equation (Formula Presented). On its small resolution and its deformation, we also consider complete cscK metrics and find that if the cscK metrics are homogeneous, then they must be Ricci-flat.

Original language	English
Pages (from-to)	1215-1233
Number of pages	19
Journal	Communications in Mathematical Physics
Volume	335
Issue number	3
DOIs	https://doi.org/10.1007/s00220-015-2337-5
Publication status	Published - May 2015
Externally published	Yes

Access to Document

10.1007/s00220-015-2337-5

Cite this

@article{e068c81559b241a58c5d5207b37716dc,

title = "Complete cscK Metrics on the Local Models of the Conifold Transition",

abstract = "In this paper, we construct complete constant scalar curvature K{\"a}hler (cscK) metrics on the complement of the zero section in the total space of (Formula Presented) over P1, which is biholomorphic to the smooth part of the cone C0 in C4 defined by equation (Formula Presented). On its small resolution and its deformation, we also consider complete cscK metrics and find that if the cscK metrics are homogeneous, then they must be Ricci-flat.",

author = "Jixiang Fu and Yau, \{Shing Tung\} and Wubin Zhou",

note = "Publisher Copyright: {\textcopyright} 2015, Springer-Verlag Berlin Heidelberg.",

year = "2015",

month = may,

doi = "10.1007/s00220-015-2337-5",

language = "English",

volume = "335",

pages = "1215--1233",

journal = "Communications in Mathematical Physics",

issn = "0010-3616",

number = "3",

}

TY - JOUR

T1 - Complete cscK Metrics on the Local Models of the Conifold Transition

AU - Fu, Jixiang

AU - Yau, Shing Tung

AU - Zhou, Wubin

PY - 2015/5

Y1 - 2015/5

N2 - In this paper, we construct complete constant scalar curvature Kähler (cscK) metrics on the complement of the zero section in the total space of (Formula Presented) over P1, which is biholomorphic to the smooth part of the cone C0 in C4 defined by equation (Formula Presented). On its small resolution and its deformation, we also consider complete cscK metrics and find that if the cscK metrics are homogeneous, then they must be Ricci-flat.

AB - In this paper, we construct complete constant scalar curvature Kähler (cscK) metrics on the complement of the zero section in the total space of (Formula Presented) over P1, which is biholomorphic to the smooth part of the cone C0 in C4 defined by equation (Formula Presented). On its small resolution and its deformation, we also consider complete cscK metrics and find that if the cscK metrics are homogeneous, then they must be Ricci-flat.

UR - https://www.scopus.com/pages/publications/84925518278

U2 - 10.1007/s00220-015-2337-5

DO - 10.1007/s00220-015-2337-5

M3 - Article

AN - SCOPUS:84925518278

SN - 0010-3616

VL - 335

SP - 1215

EP - 1233

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -

Complete cscK Metrics on the Local Models of the Conifold Transition

Abstract

Access to Document

Other files and links

Cite this