Sub-Riemannian geodesics and heat operator on odd dimensional spheres

Agrachev A., Boscain U., Gauthier J.-P., Rossi F.: The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups. J. Funct. Anal. 256(8), 2621–2655 (2009)

Agrachev A., Sachkov Y.: Control Theory from the Geometric Viewpoint. Springer, Berlin (2004)

Alekseevsky D., Kamishima Y.: Pseudo-conformal quaternionic CR structure on (4n+3)-dimensional manifolds. Ann. Mat. Pura Appl. (4) 187(3), 487–529 (2008)

Baudoin F., Bonnefont M.: The subelliptic heat kernel on SU(2): representations, asymptotics and gradient bounds. Math. Z. 263(3), 647–672 (2009)

Calin, O., Chang, D.-C., Greiner, P.: Geometric analysis on the Heisenberg group and its generalizations. AMS/IP Studies in Advanced Mathematics, vol. 40. American Mathematical Society, Providence; International Press, Somerville (2007)

Calin O., Chang D.-C., Markina I.: SubRiemannian geometry on the sphere $${\mathbb{S}^3}$$ . Canad. J. Math. 61(4), 721–739 (2009)

Calin O., Chang D.-C., Markina I.: Geometric analysis on H-type groups related to division algebras. Math. Nachr. 282(1), 44–68 (2009)

Capogna L., Danielli D., Pauls S.D., Tyson J.: An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem. Progress in Mathematics, vol. 259. Birkhäuser, Basel (2007)

Chang D.-C., Markina I.: Geometric analysis on quaternion $${\mathbb{H}}$$ -type groups. J. Geom. Anal. 16(2), 265–294 (2006)

Chang D.-C., Markina I., Vasil’ev A.: Sub-Riemannian geodesics on the 3-D sphere. Complex Anal. Oper. Theory 3(2), 361–377 (2009)

Chang D.-C., Markina I., Vasil’ev A.: Hopf fibration: geodesics and distances. J. Geom. Phys. 61(6), 986–1000 (2011)

Cheeger J., Ebin D.G.: Comparison Theorems in Riemannian Geometry. AMS Chelsea Publishing, Providence (2008)

Chow W.-L.: Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung (German). Math. Ann. 117, 98–105 (1939)

do Carmo, M.: Riemannian geometry. Translated from the second Portuguese edition by Francis Flaherty. Mathematics: Theory & Applications. Birkhäuser Boston, Boston (1992)

Godoy M., Markina I.: Sub-Riemannian geometry of parallelizable spheres. Revista Matemática Iberoamericana. 27(3), 997–1022 (2011)

Gromov, M.: Carnot–Carathéodory spaces seen from within. In: Sub-Riemannian Geometry. Progress in Mathematics, vol. 144, pp. 79–323. Birkhäuser, Basel (1996)

Hurtado A., Rosales C.: Area-stationary surfaces inside the sub-Riemannian three-sphere. Math. Ann. 340(3), 675–708 (2008)

Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry, vol. I. Reprint of the 1969 original. Wiley, New York (1996)

Liu, W., Sussmann, H.J.: Shortest paths for sub-Riemannian metrics on rank-two distributions. Mem. Am. Math. Soc. 118(564) (1995)

Margulis G., Mostow G.: Some remarks on the definition of tangent cones in a Carnot–Carathéodory space. J. Anal. Math. 80, 299–317 (2000)

Mitchell J.: On Carnot–Carathéodory metrics. J. Diff. Geom. 21, 35–45 (1985)

Montgomery R.: A tour of subriemannian geometries, their geodesics and applications. Mathematical Surveys and Monographs, vol. 91. American Mathematical Society, Providence (2002)

Rashevskiĭ P.K.: About connecting two points of complete nonholonomic space by admissible curve. Uch. Zapiski Ped. Inst. K. Liebknecht 2, 83–94 (1938)

Ritoré M., Rosales C.: Area-stationary surfaces in the Heisenberg group $${\mathbb{H}^1}$$ . Adv. Math. 219(2), 633–671 (2008)

Rosenberg S.: The Laplacian on a Riemannian manifold. An introduction to analysis on manifolds. London Mathematical Society Student Texts, vol. 31. Cambridge University Press, Cambridge (1997)

Sternberg, S.: Semi-Riemannian Geometry and General Relativity. http://www.math.harvard.edu/~shlomo/docs/semi_riemannian_geometry.pdf

Sussmann H.: Orbits of families of vector fields and integrability of distributions. Trans. Am. Math. Soc. 180, 171–188 (1973)