Preserving Positive Intermediate Curvature
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12220_2023_Article_1419.pdf
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Author(s)
Chow, Tsz-Kiu A.
Johne, Florian
Wan, Jingbo
Date Issued
September 23, 2023
Publisher
Springer US
Citation
The Journal of Geometric Analysis. 2023 Sep 23;33(12):366
Version
Final published version
Abstract
Abstract
Consider a compact manifold N (with or without boundary) of dimension n. Positive m-intermediate curvature interpolates between positive Ricci curvature (
$$m = 1$$
m
=
1
) and positive scalar curvature (
$$m = n-1$$
m
=
n
-
1
), and it is obstructed on partial tori
$$N^n = M^{n-m} \times \mathbb {T}^m$$
N
n
=
M
n
-
m
×
T
m
. Given Riemannian metrics
$$g, {\bar{g}}$$
g
,
g
¯
on
$$(N, \partial N)$$
(
N
,
∂
N
)
with positive m-intermediate curvature and m-positive difference
$$h_g - h_{{\bar{g}}}$$
h
g
-
h
g
¯
of second fundamental forms we show that there exists a smooth family of Riemannian metrics with positive m-intermediate curvature interpolating between g and
$${\bar{g}}$$
g
¯
. Moreover, we apply this result to prove a non-existence result for partial torical bands with positive m-intermediate curvature and strictly m-convex boundaries.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s12220-023-01419-2
