Dimensions on next world

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water + energy + food + minerals + land + manufacturing + knowledge

Geodesic — the shortest/natural path through curved spacetime.
Manifold — a space that can have different local geometries.
Metric — mathematically defines distances and intervals.
Curvature — describes how spacetime/space bends.
Topology — describes global properties such as connectedness and holes.
Hypersurface — a lower-dimensional surface embedded in a higher-dimensional space.
Fiber bundle — a space constructed from a base space and attached fibers.
Compactification — extra dimensions curled into very small geometries.
Calabi–Yau manifold — a geometry commonly used for compact extra dimensions in string theory.
� manifold — a special 7-dimensional geometry important in some M-theory compactifications.
Brane geometry — geometry associated with higher-dimensional objects (“branes”) in string/M-theory.
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If you mean 11 types of geometry/structures relevant to higher-dimensional physics, with geodesic as one example, there isn't a standard scientific list of exactly 11. But a useful conceptual list is:

  1. Geodesic — the shortest/natural path through curved spacetime.
  2. Manifold — a space that can have different local geometries.
  3. Metric — mathematically defines distances and intervals.
  4. Curvature — describes how spacetime/space bends.
  5. Topology — describes global properties such as connectedness and holes.
  6. Hypersurface — a lower-dimensional surface embedded in a higher-dimensional space.
  7. Fiber bundle — a space constructed from a base space and attached fibers.
  8. Compactification — extra dimensions curled into very small geometries.
  9. Calabi–Yau manifold — a geometry commonly used for compact extra dimensions in string theory.
  10. \(G_2\) manifold — a special 7-dimensional geometry important in some M-theory compactifications.
  11. Brane geometry — geometry associated with higher-dimensional objects (“branes”) in string/M-theory.

Important: these are not 11 dimensions themselves. They are mathematical/geometrical concepts used to describe spaces and higher-dimensional theories. A geodesic, for example, is a path, not a dimension.

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