How can I classify convex, planar and concave sub class in the curvature map?

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Ovidiu Csillik

Some useful software to derive curvature, with detailed documentation on this topic:

SAGA GIS: http://www.saga-gis.org/saga_tool_doc/2.2.3/ta_morphometry_0.html

GRASS GIS: http://wgbis.ces.iisc.ernet.in/grass/grass71/manuals/r.param.scale.html

QGIS: https://docs.qgis.org/2.14/gl/docs/user_manual/processing_algs/saga/terrain_analysis_morphometry.html

ArcGIS: https://desktop.arcgis.com/en/arcmap/10.3/tools/spatial-analyst-toolbox/how-curvature-works.htm

Landserf: http://www.staff.city.ac.uk/~jwo/landserf/landserf230/

Gabriel Asato

I think Ovidiu gave the most practical answer to your question. As result of applying those tools you obtain slopes classified by curvature. Take in account the presicion of the method depends of the DEM resolution.