Geodesic orbit Randers metrics in homogeneous bundles over generalized Stiefel manifolds

In this article, we study the geodesic orbit Randers spaces of the form <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mi>G</m:mi> <m:mo>/</m:mo> <m:mi>H</m:mi> </m:mrow> <m:mo>,</m:mo> <m:mi>F</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> {(G/H,F)} , such that G is one of the compact classical Lie groups <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>SO</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>n</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> {{S}{O}(n)} , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>SU</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>n</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> {{S}{U}(n)} , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>Sp</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>n</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> {{S}{p}(n)} , and H is a diagonally embedded product <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mi>H</m:mi> <m:mn>1</m:mn> </m:msub> <m:mo>×</m:mo> <m:mi mathvariant="normal">⋯</m:mi> <m:mo>×</m:mo> <m:msub> <m:mi>H</m:mi> <m:mi>s</m:mi> </m:msub> </m:mrow> </m:math> {H₁×⋯× Hₛ} , where <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>H</m:mi> <m:mi>i</m:mi> </m:msub> </m:math> {Hᵢ} is of the same type as G . Such spaces include spheres, Stiefel manifolds, Grassmann manifolds, and flag manifolds. The present work is a contribution to the study of geodesic orbit Randers spaces <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mi>G</m:mi> <m:mo>/</m:mo> <m:mi>H</m:mi> </m:mrow> <m:mo>,</m:mo> <m:mi>F</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> {(G/H,F)} with H semisimple. We construct new examples of non-Riemannian Randers g.o. metrics in homogeneous bundles over generalized Stiefel manifolds which are not naturally reductive. Also, we obtain the specific expressions of these Randers g.o. metrics.