This .NET class wraps the AcDbCurve ObjectARX class. 

The Curve class is the base class for all the entity classes that are variations of a curve such as Arc, Circle, Ellipse, Spline, and others. This base class provides the common functionality such as finding parameters for a point on the curve, finding offset curves, finding projections of the curve onto a plane, and so on.

Autodesk.AutoCAD.DatabaseServices.DBObject
    Autodesk.AutoCAD.DatabaseServices.Entity
        Autodesk.AutoCAD.DatabaseServices.Curve
            Autodesk.AutoCAD.DatabaseServices.Arc
            Autodesk.AutoCAD.DatabaseServices.Circle
            Autodesk.AutoCAD.DatabaseServices.Ellipse
            Autodesk.AutoCAD.DatabaseServices.Leader
            Autodesk.AutoCAD.DatabaseServices.Line
            Autodesk.AutoCAD.DatabaseServices.Polyline
            Autodesk.AutoCAD.DatabaseServices.Polyline2d
            Autodesk.AutoCAD.DatabaseServices.Polyline3d
            Autodesk.AutoCAD.DatabaseServices.Ray
            Autodesk.AutoCAD.DatabaseServices.Spline
            Autodesk.AutoCAD.DatabaseServices.Xline

Public abstract Class Curve
Inherits Entity

public abstract class Curve : Entity;

DBObject