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The present Special Issue of Symmetry is devoted to two important areas of global Riemannian geometry, namely submanifold theory and the geometry of Lie groups and homogeneous spaces. Submanifold theory originated from the classical geometry of curves and surfaces. Homogeneous spaces are manifolds that admit a transitive Lie group action, historically related to F. Klein's Erlangen Program and S. Lie's idea to use continuous symmetries in studying differential equations. In this Special Issue, we provide a collection of papers that not only reflect some of the latest advancements in both areas, but also highlight relations between them and the use of common techniques. Applications to other areas of mathematics are also considered.

warped products --- vector equilibrium problem --- Laplace operator --- cost functional --- pointwise 1-type spherical Gauss map --- inequalities --- homogeneous manifold --- finite-type --- magnetic curves --- Sasaki-Einstein --- evolution dynamics --- non-flat complex space forms --- hyperbolic space --- compact Riemannian manifolds --- maximum principle --- submanifold integral --- Clifford torus --- D’Atri space --- 3-Sasakian manifold --- links --- isoparametric hypersurface --- Einstein manifold --- real hypersurfaces --- Kähler 2 --- *-Weyl curvature tensor --- homogeneous geodesic --- optimal control --- formality --- hadamard manifolds --- Sasakian Lorentzian manifold --- generalized convexity --- isospectral manifolds --- Legendre curves --- geodesic chord property --- spherical Gauss map --- pointwise bi-slant immersions --- mean curvature --- weakly efficient pareto points --- geodesic symmetries --- homogeneous Finsler space --- orbifolds --- slant curves --- hypersphere --- ??-space --- k-D’Atri space --- *-Ricci tensor --- homogeneous space

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The description for this book, Curvature and Betti Numbers. (AM-32), Volume 32, will be forthcoming.

Curvature. --- Geometry, Differential. --- Abelian integral. --- Affine connection. --- Algebraic operation. --- Almost periodic function. --- Analytic function. --- Arc length. --- Betti number. --- Coefficient. --- Compact space. --- Complex analysis. --- Complex conjugate. --- Complex dimension. --- Complex manifold. --- Conservative vector field. --- Constant curvature. --- Constant function. --- Continuous function. --- Convex set. --- Coordinate system. --- Covariance and contravariance of vectors. --- Covariant derivative. --- Derivative. --- Differential form. --- Differential geometry. --- Dimension (vector space). --- Dimension. --- Einstein manifold. --- Equation. --- Euclidean domain. --- Euclidean geometry. --- Euclidean space. --- Existential quantification. --- Geometry. --- Hausdorff space. --- Hypersphere. --- Killing vector field. --- Kähler manifold. --- Lie group. --- Manifold. --- Metric tensor (general relativity). --- Metric tensor. --- Mixed tensor. --- One-parameter group. --- Orientability. --- Partial derivative. --- Periodic function. --- Permutation. --- Quantity. --- Ricci curvature. --- Riemannian manifold. --- Scalar (physics). --- Sectional curvature. --- Self-adjoint. --- Special case. --- Subset. --- Summation. --- Symmetric tensor. --- Symmetrization. --- Tensor algebra. --- Tensor calculus. --- Tensor field. --- Tensor. --- Theorem. --- Torsion tensor. --- Two-dimensional space. --- Uniform convergence. --- Uniform space. --- Unit circle. --- Unit sphere. --- Unit vector. --- Vector field.