Shimoda, Taishi Examples of globally hypoelliptic operator on special dimensional spheres without infinitesimal transitivity. (English) Zbl 1034.35015 Proc. Japan Acad., Ser. A 78, No. 7, 112-115 (2002). Summary: This paper gives examples of globally hypoelliptic operator on \(S^3\), or on \(S^7\), or on \(S^{15}\) which is sum of squares of real vector fields. These operators fail to satisfy the infinitesimal transitivity condition (the Hörmander bracket condition) at every point and therefore they are not hypoelliptic in any subdomain. MSC: 35H10 Hypoelliptic equations Keywords:Omori-Kobayashi conjecture; infinitesimal transitivity condition; Hörmander bracket condition PDF BibTeX XML Cite \textit{T. Shimoda}, Proc. Japan Acad., Ser. A 78, No. 7, 112--115 (2002; Zbl 1034.35015) Full Text: DOI OpenURL References: [1] Hörmander, L.: Hypoelliptic second order differential equations. Acta Math., 119 , 147-171 (1967). · Zbl 0156.10701 [2] Omori, H., and Kobayashi, T.: Global hypoellipticity of subelliptic operators on closed manifolds. Hokkaido Math. J., 28 , 613-633 (1999). · Zbl 0942.35050 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.