Algebraic dimension of twistor spaces and scalar curvature of anti-self-dual metrics

AbstractIt is shown that there exists a twistor space on the n-fold connected sum of complex projective planes nCP2, whose algebraic dimension is one and whose general fiber of the algebraic reduction is birational to an elliptic ruled surface or a K3 surface. The former kind of twistor spaces are constructed over nCP2 for any n ≥ 5, while the latter kind of example is constructed over 5CP2. Both of these seem to be the first such example on nCP2. The algebraic reduction in these examples is induced by the anti-canonical system of the twistor spaces. It is also shown that the former kind of twistor spaces contain a pair of non-normal Hopf surfaces.

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Positive scalar curvature metrics via end-periodic manifolds

Annals of K-Theory ◽

10.2140/akt.2020.5.639 ◽

2020 ◽

Vol 5 (3) ◽

pp. 639-676

Author(s):

Michael Hallam ◽

Varghese Mathai

Keyword(s):

Scalar Curvature ◽

Positive Scalar Curvature ◽

Positive Scalar

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ON THE ALGEBRAIC DIMENSION OF BANACH SPACES OVER NON-ARCHIMEDEAN VALUED FIELDS OR ARBITRARY RANK

Proyecciones (Antofagasta) ◽

10.4067/s0716-09172007000300001 ◽

2007 ◽

Vol 26 (3) ◽

Cited By ~ 1

Author(s):

HERMINIA OCHSENIUS ◽

W. H. SCHIKHOF

Keyword(s):

Banach Spaces ◽

Valued Fields ◽

Algebraic Dimension ◽

Arbitrary Rank

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On the quantization of folded strings in non-critical dimensions

Journal of High Energy Physics ◽

10.1007/jhep12(2020)120 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Jacob Sonnenschein ◽

Dorin Weissman

Keyword(s):

Scalar Curvature ◽

Space Dimension ◽

Massive Particle ◽

Open String ◽

Closed String ◽

Target Space ◽

Critical Dimensions ◽

Complete Set ◽

Rotating String ◽

Folding Point

Abstract Classical rotating closed string are folded strings. At the folding points the scalar curvature associated with the induced metric diverges. As a consequence one cannot properly quantize the fluctuations around the classical solution since there is no complete set of normalizable eigenmodes. Furthermore in the non-critical effective string action of Polchinski and Strominger, there is a divergence associated with the folds. We overcome this obstacle by putting a massive particle at each folding point which can be used as a regulator. Using this method we compute the spectrum of quantum fluctuations around the rotating string and the intercept of the leading Regge trajectory. The results we find are that the intercepts are a = 1 and a = 2 for the open and closed string respectively, independent of the target space dimension. We argue that in generic theories with an effective string description, one can expect corrections from finite masses associated with either the endpoints of an open string or the folding points on a closed string. We compute explicitly the corrections in the presence of these masses.

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Quaternionic contact 4n + 3-manifolds and their 4n-quotients

Annals of Global Analysis and Geometry ◽

10.1007/s10455-021-09758-5 ◽

2021 ◽

Author(s):

Yoshinobu Kamishima

Keyword(s):

Scalar Curvature ◽

Lie Group ◽

Contact Structure ◽

Einstein Manifolds ◽

Hermitian Metrics ◽

Kähler Metric ◽

Formula One ◽

Quaternion Space ◽

Kahler Metric ◽

Do So

AbstractWe study some types of qc-Einstein manifolds with zero qc-scalar curvature introduced by S. Ivanov and D. Vassilev. Secondly, we shall construct a family of quaternionic Hermitian metrics $$(g_a,\{J_\alpha \}_{\alpha =1}^3)$$ ( g a , { J α } α = 1 3 ) on the domain Y of the standard quaternion space $${\mathbb {H}}^n$$ H n one of which, say $$(g_a,J_1)$$ ( g a , J 1 ) is a Bochner flat Kähler metric. To do so, we deform conformally the standard quaternionic contact structure on the domain X of the quaternionic Heisenberg Lie group$${{\mathcal {M}}}$$ M to obtain quaternionic Hermitian metrics on the quotient Y of X by $${\mathbb {R}}^3$$ R 3 .

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