Geodesic
Systolic Inequalities for Compact Quotients of Carnot Groups with Popp's Volume
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we give a systolic inequality for a quotient space of a Carnot group $\Gamma\backslash G$ with Popp's volume. Namely we show the existence of a positive constant $C$ such that the systole of $\Gamma\backslash G$ is less than ${\rm Cvol}(\Gamma\backslash G)^{\frac{1}{Q}}$, where $Q$ is the Hausdorff dimension. Moreover, the constant depends only on the dimension of the grading of the Lie algebra $\mathfrak{g}=\bigoplus V_i$. To prove this fact, the scalar product on $G$ introduced in the definition of Popp's volume plays a key role.
Keywords: sub-Riemannian geometry, Carnot groups, Popp's volume, systole. 
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     author = {Kenshiro Tashiro},
     title = {Systolic {Inequalities} for {Compact} {Quotients} of {Carnot} {Groups} with {Popp's} {Volume}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a57/}
}
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Kenshiro Tashiro. Systolic Inequalities for Compact Quotients of Carnot Groups with Popp's Volume. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a57/

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